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An integrable semi-discretization of the two-component Hunter-Saxton equation
Energy localization in damped nonlinear disordered metastructures under superharmonic resonance
On the quasi-continuum approximation of some localized patterns in the FPUT lattice
Temporal dissipative solitons and optical frequency combs in coherently driven Kerr resonators
Existence of solutions for elliptic problems involving the $(1,q)$-Laplacian operator and a discontinuous superlinear nonlinearity
Generalized Morrey-Campanato estimates for elliptic equations with coefficients of integrable oscillation
Spectral stability in the modified Camassa-Holm equation
Minimizers for Coulomb gases constrained to a halfspace
Supratransmission in Lattices with Purely Nonlinear Coupling
Complete Classification and Nondegeneracy of $N$-Component Cubic Nonlinear Schrödinger System in ${\mathbb R}$
Local and global well-posedness in the $L^2$-setting for the Q-tensor model in $\mathbb R^N$ and $\mathbb R^N_+$
Random Tensor Estimates and Deterministic Diagonal Resolutions for Mixed Paracontrolled Operators
The Hall problem in domains
Harmonic immersions of the Sierpinski gasket into the hyperbolic plane
Asymptotic dynamics of inhibitory networks for the NNLIF Model in the large-delay limit
The Vanishing Viscosity Limit and Boundary Layers for Symmetric Fluid Flows with Anisotropic Viscosity
On the Darboux-Halphen system: Jacobi vs Lie
Determining the unbounded potential in the two-dimensional Schrödinger equation from Cauchy data
Flow kinematics for equatorial coupled surface and internal waves
Finite-Window Local-to-Clean Transfer and Anti-Phantom Detection for Sharp Navier-Stokes Packages
Chaos from quantum bath fluctuations
Comparing Deterministic and Stochastic Parameter Recovery Algorithms Applied to Chaotic Systems
Probing chaos and thermalization through out-of-time-ordered correlators in random field spin chains
Topological spectral form factor reveals emergent non-Hermitian single-particle $\mathcal{PT}$ transitions from many-body quantum chaos
Two weight estimates for difference quotients
The Parabolic Harnack Inequality on Weighted Riemannian Manifolds
Norm inflation for the cubic hyperbolic NLS on $\mathbb T^2$
Rigorous analysis for the Dirac system on the quarter-plane
Vector peakon equations and isospectral flows in Clifford algebras
Trudinger-Moser type inequality in fractional Sobolev space with singularity on smooth submanifold
The Absorption Theorem for the Beltrami-Vekua Normal Form
Inverse problems for a nonlinear dynamical Schrödinger operator with magnetic potential
Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method
Quasi-material finite-time rotationally coherent sets in photospheric supergranulation
Convergence to self-similarity for a degenerate parabolic equation with fast-growing spatially-dependent absorption
Maximal regularity and caloric trace estimates in mixed Lebesgue norms for the heat equation
Boundary value problems for some quasilinear parabolic equations under minimal conditions on the coefficients
Nonexistence for screened Hartree energies
Tamed Feynman-Kac diffusion processes: Killing-branching intertwine
Moving Boundary Problems for a Cuspon Equation and Reciprocal Associates: Exact Solution via Painleve' Symmetry Reduction
Physical completion of the Navier-Stokes equations
Anisotropic Cylindrical Waves in a Square Lattice of Acoustic Waveguides
The Extended KdV Equation: Augmented Lagrangian and Variational Solitary Waves with Applications to Dispersive Hydrodynamics
Dynamics and stabilization of topological edge solitons in driven-damped nonlinear SSH lattices
Nonlinear Localized States on a Pyrochlore Lattice
Integrable motion of curves associated with the Fokas-Lenells equation and related spin system
Rigidity Estimate for Hyperbolic Shells and its Application in $Γ$-limit Theory
Some quasilinear minimization problems involving Hardy potentials
Ground state solutions to Born-Infeld-Choquard problem
On the control of high Sobolev norms for the Wave equation on $\mathbb{T}^d$ over exponentially long times
Diagnosing the conditional-mean barrier in scientific machine-learning surrogates
Finite-Window Computational Anti-Phantom Theorems for Scale-Critical Navier-Stokes Defects
Towards a Floer theory for Mars II -- Floer Hessian field almost extends
Strong ill-posedness of the 2D Boussinesq equations in supercritical Besov spaces
Borderline gradient continuity for degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms
Threshold dynamics for the $3d$ radial cubic NLS with repulsive inverse-square potential
Mathematical Analysis of Subwavelength Resonances and Gradient Blow-up for Two Close-to-Touching Inclusions within the Two-Dimensional Elasticity
Uniqueness of the blow-up for some Alt-Phillips cones
Reconstruction of time-dependent coefficients in a semilinear dynamical Schr{ö}dinger equation
Segregated solutions of a degenerate cross-diffusion system with drifts
Mirror flows and $p$-Laplacian eigenvalue problems on metric measure spaces
Identification of an inclusion from local Cauchy data for time-harmonic elastic waves
Elliptic Harnack inequality and Poincaré inequality for $p$-energies on metric measure spaces
Semiclassical periodic-orbit theory for quantum spectra
Dispersal-induced survival of predators in metacommunities due to transient chaos
More on Classical Stability of Hopf-like Solitons of the Toroidal-Twisted type
Emergent population dynamics of random walkers with cooperative reproduction and spatial selection
From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability
Integrable hierarchies with zero dispersion and elliptic curves
Negative Hierarchy of Hydrodynamic Type Equations
Dimer models on astroidal zig-zag graphs
Whitham modulation equations for the regularized Boussinesq equation with cubic nonlinearity
Measuring qualitative change: A variational score for tracking dynamical shifts in partial differential equations
Benjamin-Ono dynamics of internal waves with currents
Critical Ledgers and Scale-Defect Cascades for Navier-Stokes
A new resolution space for nonlinear Schrödinger equations and applications
On the gauge-invariant dynamical charges and densities of the 1-instanton solution
A study of variational single solitary waves governed by the conservative-extended KdV equation with applications to shallow water dispersive shocks
Localized inhomogeneity and position-dependent stability of migratory bird formations
Tricriticality and chaos in a generalized Allee-logistic map
Hybrid Dynamics of Rocking Blocks Beyond Overturning: Saltation Analysis, Bifurcations, and Stability Characterization
Statistical Methods for Determining Turbulence in Supercontinuum Generation
Large-space and large-time asymptotics for the mKdV soliton gas with any odd genus
Interaction-Phase Dynamics and Spectral Organization in Damped Higher-Order Nonlinear Schrödinger Models
Exact Lyapunov spectra of affine cellular automata and the parity rule on networks
Wave turbulence theory of odd fluids and solids: kinetic equations and solutions
Optimal minimax formula for bounds on ensemble averages of statistically stationary three-dimensional Navier-Stokes flows
Potential Estimates and Hodge Systems with $L^1$ data on compact manifolds
Nonuniform relaxation oscillations near SNIPER bifurcations
Lie symmetry classification and group invariant solutions of generalized radial heat equation with nonlinear reaction source
Solving models with generalized free fermions II: Path-product expansion and conserved charges
A mean field approach to multiple, long-delayed systems
Instabilities in a Non-KAM System via Information Scrambling: A Note
Bifurcation and Chaos in S-I-S Epidemic Model
Calculation of solitons derived from quivers
Exact Relevant Stress-Tensor Flows and a Causality No-Go in Self-Dual Electrodynamics
Volterra-Bogoyavlensky lattices and solutions of $A_{2n}^{(1)}$ invariant Painlevé equations
Dirichlet eigenfunctions have non-zero mean for generic domains
Local and global strong solutions to a reduced model for inviscid micropolar fluids
Some results for a stationary Navier-Stokes equation with a rough drift in a weighted functional framework
Mean-field imitation dynamics on fast assortative networks
On the weak formulation of Prandtl's minimum drag problem
Self-similar imploding solutions of the 1D compressible Euler equations with a far field cutoff
Elliptic criticality versus Volterra memory in indirect chemotaxis cascades
Well-posedness and Stability Analysis of Suspension Bridge Models Coupled with Cattaneo Heat Conduction: The Role of Viscoelastic Memory
Numerical inverse scattering transform for the coupled modified Korteweg-de Vries equation
On Killing tensors on Riemannian symmetric spaces
Bilinear formalism for Schwarzian KP and Harry Dym hierarchies
Pearl supratransmission in a boundary-driven two-dimensional nonlinear Schrödinger equation with a hole
Self-similar asymptotics in the decay problem for the Volterra lattice with zero boundary condition
Real-Time Visualization of the Spatiotemporal Dynamics of 3D Solitons
Turing patterns on non-fluctuating surfaces under mechanical stresses
Dirac monopole potentials with high charges underlying nonlinear waves
Quantum scattering of droplets by wells and barriers in one-dimensional Bose-Bose mixtures
Bound states of solitons in fiber lasers
Complete Weierstrass elliptic function solutions for coherent couplers and their relation to degenerate four-wave mixing
Adjoint inverse design of microresonator frequency combs
Patterned fronts in the wake of a parameter ramp in the complex Ginzburg Landau equation
Pattern Formation with Two Length Scales: Spatiotemporal Chaos
Long-time Asymptotics of a Full Camassa-Holm Soliton Gas
Global weak solutions of a one-sided degenerate Cahn-Hilliard model for traction-driven digit morphogenesis
Quantum Limits of the Laplacian perturbed along a geodesic on $\mathbb{S}^{2}$
A characterisation of $\infty$-harmonic maps in terms of $1$-currents
Stability of localized solutions to lattice dynamical systems
Collision Dynamics of False-Vacuum Oscillons
Temporal Matrix Scale Invariance and the Classification of Tipping Points
Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems
A symmetry theorem for localizable steady solutions of the 3D Euler equations
Branching-selection particle systems and inverse first passage problems
Hadamard ill-Posedness of the linearised Prandtl Equations in Gevrey spaces
Nash's theorem via Günther's trick
Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder
Self-propulsion in the 1D swarmalator model
Complexity synchronization as a diagnostic and control principle for adaptive systems
Random Matrix Theory for Chaotic Wave Scattering and Transport
Global Mild solutions for the fractional Navier-Stokes-Boussinesq equations in critical Fourier-Herz-Lorentz spaces
A Sign-Changing Poisson Kernel for a Non-Symmetric Elliptic Operator in a Bounded Domain
Analysis of the Quasi-Static Maxwell Equations in Resistive Solid-State Particle Detectors
The effect of geometric focusing on dispersive estimates for Schrödinger and wave equations
On a continuity method for Dirichlet problem of Hessian equations
Stability of the critical constant steady state of a Keller--Segel model
Schur Visibility and Anti-Phantom Reduction in One-Component Navier-Stokes Degeneration
Schauder-type Estimates and Log-Critical Well-posedness for the Two-Phase Muskat Problem with Surface Tension
Energy-Modulated Time-Asymmetric Spontaneous Collapse: Forward-Backward Dynamics from Stochastic Ito Reversal and Bright Solitons
Generalization of a localized-state formation mechanism in finite lattices with interaction nonlinearity
Mean-field models for morphogenetic processes in physiological contexts
On product estimates in Besov-Morrey spaces and stationary solutions for the Hall-MHD and Navier-Stokes systems
Strong Ill-posedness of the 2d Incompressible Euler Equation in Critical Besov Spaces
Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp $L^2$ stability and $L^p$ extensions
Scalene Yang-Baxter maps and Lax triples
The quantum group structure of long-range integrable deformations
Separatrix Splitting and Chaotic Dynamics in Collective-Coordinate Reductions of Driven $φ^4$ Kinks
Dispersive estimates for wave-type equations with time-dependent damping
Well-posedness and stability for a thermoelectromagnetic system
Unidirectional Entropic Solutions of the Pressureless Euler Alignment System
Boundary rectifiability and compactness of integral currents via $BV$ functions
Space-time excitation creates soliton trains in multimode fibers
Principal eigenvalues, maximum principles and estimates for Lane-Endem related systems in nondivergence form
Boundary Harnack estimates of optimal order for kinetic Fokker-Planck equations
Cell-cell adhesion and multiphase Hele-Shaw problem as the singular limit of a Keller-Segel system
Chaos in cymatics-inspired Gaussian landscapes
Forward Construction of Vacuum Initial Data with Borderline Decay
Asymptotic Profiles and Non-Trivial Breathers in Kahler-Ricci Flow
Boundedness and evolution rates for a quasilinear reaction-diffusion equation
Hypothetical Singularity of 3D Navier-Stokes in Clay Institute set up Reduces to Axisymmetric with Swirl class
Local Boundedness of Local Minimizers for a Class of Nonlinear Elliptic Systems with General Growth
A New Level Set Formulation for Improved Dirichlet Eigenvalue Minimizers
Homogenization in fractional phase transitions at the critical scale
Integrability of oscillators and transcendental invariant curves
A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation
The $L^p$ Neumann problem for parabolic operators with coefficients satisfying small Carleson condition
Benjamin-Feir spectrum of hydroelastic Stokes waves
Linear Stability of the Lamb-Chaplygin Dipole
High Mach number limit of the compressible Navier--Stokes equations in critical Besov spaces
Thermal Relaxation Effects on Stability Thresholds: A Comparative Analysis of Thermoelastic Timoshenko-Boltzmann Systems Under Fourier and Cattaneo Laws
Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball
Rogue waves for semilinear wave equations
An optimal local theory for reaction-diffusion equations driven by non-trace-class noise
Invariant measures for the one-dimensional stochastic Navier-Stokes-Korteweg equations
Minimizing clusters with prescribed asymptotic geometry
On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I
On a rod-Kadomtsev-Petviashvili shallow water equation in two dimensions
Euler Immersion
Self-improving properties for a class of elliptic and parabolic equations on bounded domains
Determination of radial nonlocal nonlinearities from the scattering map
Widespread quasi-steady state assumption in biological interaction modeling mischaracterizes system transitions
Gaussian decay for the Harmonic oscillator
Well-posedness and finite element approximation of the electrostatic shear Alfvén wave equations
$L^2$-boundedness of the $n$-th Calderón commutator on Lipschitz graphs
Loop Current Extension as an Effective Delayed Dynamical System
Phase lag enhances synchronization in coupled oscillators with inertia
Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series
Thin Domains, Reduction, and Slow Manifolds
Robust interpolation inequalities via Chebyshev-type integral inequalities
Solutions to critical equations with a superposition of nonlocal Hartree-type nonlinearities
Interface problems of mixed spatial order
Exponential Time Differencing Schemes for a Phase-Field Model of Multicomponent Membranes
Soliton gas resolution and statistics of random wave fields in semiclassical integrable turbulence
Global Analytical Solution of the Identical Kuramoto Model for N=3 via Koopman Eigenfunctions
Bregman divergences and error control via convex duality
Quantitative Homogenization Theory for Lamé-Stokes Coupled Systems
Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network
On singular solitons of the KP equation and the Go-diagrams
Novel periodic solutions and rogue waves of the defocusing scalar and coupled Ablowitz-Ladik systems on a nonzero background
Equivariant Quantum Cohomology of Grassmannians via the Clifford algebra
Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections
Empirical One-Step Conditional Entropy in Infinite Ergodic Systems: Vanishing Entropy Rate, Sparse-Transition Scaling, and Mittag-Leffler Fluctuations
Synchronization of topological signals in higher-order adaptive multilayer network
Existence of the C-type renormalisation two-cycle
Many-Body Quantum Chaos At All Time Scales
Lagrangian Ellipsoid Diagnostics for Stochastic Hydrodynamics: Source--Sink Modeling of Deforming Particle Clouds
Effects of stickiness in quantum chaotic billiards with $n$-fold symmetry
Fractional Sobolev embeddings on noncommutative torus
Legendrian cycles and Reilly-type variational formulae for $F_nW^{2,n}$-sets
Eventual regularity and asymptotic behavior of Leray-Hopf weak solutions for the Hall-MHD system
Remarks on selection problems for first-order discounted mean field games
Moving Boundary Problems for a Cuspon Equation and Reciprocal Associates: Exact Solution via Painleve' Symmetry Reduction
Mixed Global Dynamics of the Forced Vibro-Impact Oscillator with Coulomb Friction and its Symplectic Structure, KAM Tori, and Persistence
Recovering stable kernels from exterior measurements
An inverse source problem for a fully nonlinear elliptic equation
Large data scattering for the defocusing $k$-dispersion generalized Benjamin-Ono equation in the energy space
Homeomorphic modified wave operators for the Vlasov-Poisson system
Construction of multi-bubble solutions for the energy-critical wave equation in dimension four
The Free Lunch Theorem of Homogenisation
Calibration energy and mean curvature flow
The Ginzburg-Landau system with general potential: maximum principle and gradient estimates
Quenched Dipole Pairs in Viscous Fluid Membranes across the Saffman Crossover: Integrable Hamiltonian Dynamics
Spin-Hair Induced Chaos of Spinning Test Particles in Rotating Hairy Black Holes
Reconfigurable Nonlinear Photonic Networks for In-Situ Learning and Memory Formation via Driven-Dissipative Dynamics
A comparative study of accuracy and rollout stability of temporal surrogate models
Beyond descendants: integrable observables for cohomological field theories
Dynamic solutions of next generation neural field models with delays
Birth and metamorphoses of resonances in the driven van der Pol oscillator
A variational approach to ferronematics with a dimension reduction
Convergence to global equilibrium for the semiconductor Boltzmann equation
Harnack inequality for superposition operators of mixed fractional order
Dynamical frustration in space-time metamaterials
Exact Charge, Current, and Velocity Fields of Interacting Korteweg-de Vries Solitons
Observation of interaction-induced fast Thouless pumping of solitons
On a class of critical Schrödinger-Poisson systems involving the (p,q)-Laplacian
Generalized Kontsevich model, topological recursion, and $r$-spin theory
Strichartz Estimates and Small-Posedness Global Well-Posedness for the Periodic Quintic NLS in 1D
Analytical Solutions of 3D Maxwell's Equations via Infinite-Order Curl-Operator Expansions
Classification of blow-ups for the Alt--Phillips problem in three dimensions
Canonical separating coordinates in the generalized cubic Hénon-Heiles systems
Orlov-Schulman symmetries of the self-dual conformal structure equations
Breakdown of Adiabatic Scaling and Noise-Induced Functional Synchronization in Deeply Quiescent Excitable Systems
Computing with the complex nonlinear dynamics of an optomechanical oscillator
Exponential thermalisation of viscous fluids on negatively curved manifolds
Existence of free boundary minimal disks in convex regions
Physical-Space Scarring in Generic Bunimovich Stadia
Weak-strong uniqueness and low Mach number limit for a viscous compressible fluid around a rotating body
Well-posedness and longtime behavior of the conserved Navier--Stokes--Allen--Cahn equations with unmatched viscosities and singular potential
Admissibility criteria for normal traces and Cauchy fluxes
Monotonicity of the bifurcation curve for supercritical elliptic problems in the borderline dimension $N=10$
Existence results for nonlinear cone degenerate Laplace equations
Robustness of Valley-Hall Interface Modes Against Sharp Bending
Water-at-Rest Equilibrium Stability Analysis of a first-moment Shallow Water Exner Moment Model with Sediment Entrainment and Deposition: Extended Technical Report
On a Class of Continuous Collision-Induced Breakage Equation
Global Existence and Incompressible Limit for the Two-Dimensional Compressible Navier-Stokes Equations in a Half-Space with Large Initial Data and Vacuum
Regularity and reentry basins of low Earth orbits in the $J_{2}$-solar radiation pressure problem
Jet-Density of Finite-Gap Solutions for Classes of BKM Systems
Spherical singularities in compactified Ruijsenaars--Schneider systems
Quasineutral Plasmas and the Geometry of Kinetic Stability
Towards a Fundamental Principle for $λ$-Homogeneous Solutions on Cones
Minimal surfaces with rapid area growth
On a fractional $p$-Laplacian problem in the whole space and with singular reaction
1.4 Time-periodic systems of differential equations
Dissipative systems generating any structurally stable chaos
Constrained integrability and anyonic chains
A non-commutative discrete first Painlevé hierarchy: the Lax pair approach
Hidden Ising models from the generalized Yang-Baxter equation
Collective dynamics of active matter with orientation-weighted alignment
Chaos to Synchronization and Dissipative Quantum Scarring in Open Coupled top-Dicke model in a Lossy Cavity
Self-Generated Chiral Rotation in Whispering-Gallery Optomechanics
Classification of Planar Systems
Dark solitons in nonlinear Su-Schrieffer-Heeger lattices
Chiral solitary waves in a nonlinear topological insulator model
Generalized PT-symmetric nonlinear Dirac equation: exact solitary waves solutions, stability and conservation laws
AI models of unstable flow exhibit hallucination
Arbitrary-genus dark soliton gases in the defocusing nonlinear Schrödinger hydrodynamics
Rogue wave statistics and integrable turbulence in the Gerdjikov-Ivanov equation
Patterns in Time and Space from a Single Morphogen via Nonlinear Layering
Maximal entropy production principle and the Euler system of gas dynamics
Hybrid Ermakov-Ray-Reid/Painlevé II Symmetry Reduction: Application to a Class of Moving Boundary Problems
Regularity of solutions of the Dyson equation and applications
Backward Uniqueness for Coupled Ultraparabolic Operators and an Application to Jerk-Driven Control Models
Resonant interactions in the $α$-FPUT lattice with site-dependent coefficients
Stability of Quadratically Regularized Optimal Transport
Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five
Liouville type theorems for fully nonlinear elliptic equations in exterior domains in half spaces
Frustrated Fields: Statistical Field Theory for Frustrated Brownian Particles on 2D Manifolds
Stochastically perturbed billiards: fingerprints of chaos and universality classes
Approximate Invariant Analysis: An Efficient Framework for Nonlinear Beam Dynamics, Part I: Geometric Approaches of the Poincaré Rotation Number
Reservoir Computing with a single Josephson junction
Complex-valued modified Zakharov Kuznetsov equation
Liouville theorems for $p$-Laplacian equations in convex cones without finite-energy condition
Modified Scattering for the Time-Dependent Kohn--Sham Equation
High-order time splitting methods for the nonlinear Gross-Pitaevskii equation
A Regularized Shallow Water System
Torsional Rigidity and Spherical Deficit for a Dirichlet Problem on Riemannian Manifolds
Holographic X-ray Phase Contrast Imaging with Partial Coherence: Uniqueness and Reconstructions from Intensity Correlations
Eigenvalue bounds for quantum dot Dirac operators
The Hidden Symmetries of Yang-Mills Theory in (1+1)-dimensions
Dynamics of wavepackets and entanglement in many-body kicked rotors under quantum resonance
On the discrete Painlevé equivalence problem, non-conjugate translations and nodal curves
Open WDVV equations and $\bigvee$-systems
Conformation dynamics in asymmetric chain-like three-body bead-spring models
Characterization of Chaotic and Homogeneous coexisting dynamics of a Memristive Thermo-Controlled MEMS
Complex network topological and spectral determinants of extreme events
Symmetry restoration through chaotic hysteresis in a non-Hermitian optical trimer
Pointwise behavior of SU(1,1) nonlinear Fourier transform
On the axisymmetric Navier-Stokes flow passing a cone with the total-slip boundary condition
Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications
On the Hersch-Weinberger inequality in higher dimensions
Coexistence of two distinct rogue wave patterns in the coupled nonlinear Schrödinger equation
On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations
Solitonic Construction of Artificial Neural Networks from Nonlinear Field Theory
Dark-Soliton Branch Blocking in Transonic Bose--Einstein Condensate Flows
Localized inhomogeneity and position-dependent stability of migratory bird formations
Generalized Error Bounds in the Recovery of Solitary Wave Profiles
Front propagation in non-homogeneous $φ^4$ model
Pairwise Distance-Diffusion Analysis (PDDA): A Geometric Framework for Estimating Hurst Exponents in Multivariate Long-Memory Processes
Data-driven system identification for piecewise dynamical systems via Sparse Identification Neural Ordinary Differential Equations
Strong Trajectorial Ontological Differentiation: A novel approach to unravel phase-space structures
Multi-Scale Coherence of Represented Flows
A Differentiable Programming Framework for Accurate and Stable Reduced-Order Modeling of Chaotic Flows
Semiclassical foundation of universality in chaotic quantum circuits
Spatiotemporal Structures of Parametrically Driven Nonlinear Lattices
Interaction-Phase Dynamics and Spectral Organization in Damped Higher-Order Nonlinear Schrödinger Models
x-periodic Quasi One Dimensional Anomalous (Rogue) Waves in Multidimensional Nonlinear Schrödinger Equations: Fission, Fusion, and Recurrence
Stability of dispersive boundary layers for scalar conservation laws in one space dimension
Inferring bifurcation diagrams of two distinct chaotic systems by a single machine
Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane
Delayed control driven oscillations in plant roots
Quantifying the safe operating space for the Amazon rainforest under climate change and deforestation
On hybrid dynamical systems of differential–difference equations
Bohmian Trajectories in a Bistable Potential Well
Transmitted and Storage-Dominated Resonance in Fractionally Damped Unidirectionally Coupled Duffing Oscillators
From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near $T_{\rm c}$ in the Non-Magnetic Case
Quantitative Einstein relation for reversible diffusions in a random environment
Boundary stabilization of an Euler-Bernoulli beam with axial force and internal delay
Quantitative Stability of Generalized $p$-Area Minimizing Surfaces
Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method
Precise asymptotic estimates and non-degeneracy of solutions to a biharmonic problem with large exponents in dimension four
Global uniform regularity and vanishing vertical viscosity limit for the compressible Navier--Stokes equations in the half-space
Optimal semiconcavity with fractional modulus for Hamilton-Jacobi equations with Neumann boundary conditions
Fourier--Galerkin Methods for Subwavelength Resonances in 2D Acoustic Metamaterials
Nonlinear Transmission Eigenvalue Problems with Nonhomogeneous Operators of Different p-Growth
Strange attractors for differential delay equations
Breathing and Rotobreathing Cyclops States in Phase Oscillators with Inertia and Two-Harmonic Coupling
Observation of sine-Gordon-like solitons in a spinor Bose-Einstein condensate
Permanent and Transient Synchronized Chaos in Large Arrays of Complex-Coupled Semiconductor Lasers
Optimizing Reservoir Computing for Reconstructing Ergodic Properties
Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry
Global estimates on the Brenier map
Asymptotic behavior of solutions for the nonlinear Hartree equation involving the fractional Laplacian
Pointwise Estimates Near Singular Sets for Quasilinear Elliptic Equations
Table of Contents
Ordinary differential equations of Morse-Sturm type
Characterizing chaos in a type of fractional Duffing's equation
CHAPTER 1. First-Order Differential Equations and Their Applications
CHAPTER 2. Linear Second- and Higher-Order Differential Equations
Liouville integrable Lotka-Volterra systems
Duality of operator Frobenius algebras and solution of Eisenhart-Stäckel problem in the non-diagonal case
From hyperbolic to complex Euler integrals
The Roaming Bethe Roots: An Effective Bethe Ansatz Beyond Integrability
A note on several inverse problems with generally random coefficients
Moment bounds on correctors for the degenerate random conductance model
The linear Cahn-Hilliard equation with an interface
Pointwise bounds and obstructions to blowup for the Landau and Boltzmann equations
Rare transitions between collective states in an active fluid via a weakly nonlinear reduction
A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation
Geometry-induced pulse dynamics in a bulk-surface reaction-diffusion system for cell polarization
Asymptotic Analysis of discrete nonlinear localised modes in a Kagome lattice
Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Physical completion of the Navier-Stokes equations
What We Talk About When We Talk About Dissipative Quantum Chaos
Data-Driven Reduced Modeling of Delayed Dynamical Systems via Spectral Submanifolds
The gauge action on semi-discrete Lax representations and its invariants
Orthosymplectic quantum groups revisited
Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials
The Korteweg-de Vries limit for the global dynamics of the Toda lattice
Global remote sensing reveals vegetation clustering as a physical footprint of shifting aridity trends in drylands
Spiral, target, stripe, and disordered waves in active six-state Potts models
Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition
Rogue-wave and lump patterns associated with the third Painlevé equation
On the kinetic $p$-Laplace equation with nonlocal diffusion
Ground states of the defocusing nonlinear Schrödinger equation with a point interaction in dimensions 2 and 3
Experimental detection of inclusions for the time-harmonic elastic wave equation
Modified Painlevé systems with meromorphic solutions for polynomial Hamiltonians of all degrees
Landau-Ginzburg models of generalised Dubrovin-Zhang form and pole collision: Dynkin-type A
Semi-global symplectic invariant of the champagne bottle
Moving Boundary Problems for a Cuspon Equation and Reciprocal Associates: Exact Solution via Painleve' Symmetry Reduction
First-Order Differential Equations and Their Applications
Homoclinic and heteroclinic solutions of the nonlinear Schrödinger equation with a complex Wadati potential
Benchmarking CNN- and Transformer-Based Models for Surgical Instrument Segmentation in Robotic-Assisted Surgery
Slow-moving pattern interfaces in general directions for a two-dimensional Swift-Hohenberg-type equation
Spectral thermodynamics of a soliton heat engine
Periodic and quasiperiodic traveling waves in nonlinear lattices with odd elasticity
Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation
Dark solitons in the fractional NLS equation
On the Riemann problem for the Adlam-Allen model
Reconstructing resonant phase oscillator interactions from noisy time series
Classification of Chimera States via Fourier Analysis and Unsupervised Learning
Revealing dynamics of non-autonomous complex systems from data
ChaosNetBench: Benchmarking Spatio-Temporal Graph Neural Networks on Chaotic Lattice Dynamics
Non-Floquet oscillations of a parametrically driven rigid planar pendulum
Material coherence and life cycle of a wildfire-generated stratospheric vortex
Physics-Informed Temporal U-Net for High-Fidelity Fluid Interpolation
Chaotic Billiard Lasers
Global well-posedness of the linearized R13 moment equations with Onsager boundary conditions
Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians
A conservation-consistent boundary condition for nonlinear models of soluble-surfactant-laden falling films
Maximal inequalities and Riesz transforms for vector-valued magnetic Schrödinger operators
Experimental Acquisition and Verification of Spectral Signatures of Dynamic Bifurcations
Coupled Arnol'd cat maps on circulant graphs
Investigation of Chaotic Behavior in Clapp Oscillator
High-throughput full-f gyrokinetics of the tokamak boundary
Boundary Blowup Solutions for the Finsler p-Laplacian: Wellposedness and Asymptotic Behaviour
Convergence of the Chern-Ricci flow on complex minimal surfaces of general type
On the non-stationary Navier-Stokes flows and reiterated homogenization
Global existence and stability of solutions for the 2D non-resistive compressible MHD system
Contents
Chapter 4 Monotone Dynamical Systems
The Laplace Transform
Differential and Difference Equations as Dynamical Systems
Essential spectrum for the $p-$Laplacian
Long-Time Stability Analysis for Stochastic Evolution Equations with Multiplicative Noise
On the $L^{2}$ estimates of the diffusion waves
Universal thin-shell limits for the viscous operator on Riemannian hypersurfaces
Nonautonomous systems of evolution inclusions
Integral Equation Methods for Scattering by Multifractal Obstacles
A Spline-based Physics-Informed Numerical Scheme: Accurate Smooth Solutions for Differential Equations
Flowing to free boundary minimal surfaces
Multipole series and differential equations
Planar Dynamical Economic Systems
Differential Equations and Modeling of Dynamical Mechanical and Biomechanical Systems
CHAPTER 4. An Introduction to Linear Systems of Differential Equations and Their Phase Plane
Nonlocal thermal Willis coupling in laminated conductors
Leray--Hopf Type Weak Solutions for the Three-Dimensional Beris--Edwards System with Stable Landau--de Gennes Potential
Newton's problem of minimal resistance in Lorentz-Minkowski space
Global Well-posedness of the 2D Stochastic Self-consistent Keller-Segel-Navier-Stokes System with Subcritical Cellular Mass
Inverse scattering theory for the discrete PT-symmetric nonlocal nonlinear Schröinger equation under arbitrarily large nonzero boundary conditions
5d Higgs branch and instanton magnetization
Finite-time blow-up of two $(1+1)$D systems rigorously derived from the 3D axisymmetric Euler equations
Discovery of Symbolic Hamiltonian Expressions with Buckingham-Symplectic Networks
From classical Lax ODEs to quantum integrable theories: the moduli
Page Curve for Local-Operator Entanglement from Free Probability
Understanding Task Performance of Time-Multiplexed Optical Reservoir Computing via Polynomial Expansion
Grünwald--Letnikov Memory Truncation in a Fractional Duffing Oscillator: Coherence Loss and Effective Delay Complexity
Unsteady, Non-Linear, and Chaotic Systems
Linear Systems of First-order Differential Equations
Differential Equations: Fundamentals, Solution Methods, and Applications in Dynamical Systems and Chaos Theory
On the Stability of Inverse Conductivity Problem for Polyhedral Inclusions under a Single Measurement
Variational derivation of the Flamant solution for a nonlinear elastic wedge
A fully averaged poroelastic Kirchhoff plate interacting with an incompressible, viscous fluid: analysis and numerical simulation
Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle
Neuromorphic Computing Based on Parametrically-Driven Oscillators and Frequency Combs
From order to chaos: Bifurcations and parameter space organization in an analog Duffing-Holmes circuit
Quantum many-body operator cascade as a route to chaos
Skillful Global Ocean Emulation and the Role of Correlation-Aware Loss
Symmetry and Rigidity Results for the Mean Field Equation and Hawking Mass on ( \mathbb{S}^2 )
A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities
Bilinear control to trajectories of 1D degenerate parabolic equations in moving domains
Well-posedness of the obstacle problem for generalized Dean-Kawasaki equation
Preface
Index
Bibliography
Front Matter
A New Way to Synchronize Memory Chaos
Unique continuation inequalities for the Dunkl-Schrödinger equation via uncertainty principles
The omnidirectional trace in H 1 ($Ω$)
Stability of Anomalous Dissipation for the Forced 3D Navier--Stokes Equations under Geometric Perturbations
Sharp error estimates in stochastic homogenization of parabolic systems with time-dependent coefficients
Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity II: 3D Profiles, Blowup, and Limiting behavior
Noether symmetries and conservation laws of a class of time-dependent multidimensional nonlinear wave equations
Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity I: $C^{\infty}$ 1D Limiting Profiles
Regularity of superposition operators of mixed fractional order
Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model
Horizon-Constrained Rashomon Sets for Chaotic Forecasting
The thermodynamic efficiency of coupled chaotic dissipative structures
Possible fractal nature of accretion flows in MAD and SANE simulations: Implications to GRS 1915+105
Nonlinear Systems of Differential Equations in the Plane
Mostly Nonlinear First–Order Differential Equations
Closed Orbits and Limit Sets
CHAPTER 6. Nonlinear Systems of Differential Equations in the Plane
Nonlinear stability of continuously self-similar naked singularities for the Einstein-scalar field equations II: linearized stability
On the Role of the Viscosity Parameters in the Large Time Asymptotics of 2D Micropolar Flows
Asymptotic profiles and large-time behavior for 3D micropolar fluid equations with possibly vanishing spin viscosity
Nonlinear stability of continuously self-similar naked singularities for the Einstein-scalar field equations I: main results
The Supersymmetric Origin of Chaos and its Hidden Topological Order
Computing with the complex nonlinear dynamics of an optomechanical oscillator
Ergodic and Discrete Time Crystal Phases in Periodically Kicked Many-Body Quantum Systems: An Analytical Study
Comment on `On computing quantum waves exactly from classical action'
A dynamical systems result on asymptotic integration of linear differential systems
Lagrange’s Equations
СИНФАЗНЫЕ И ДИФФЕРЕНЦИАЛЬНЫЕ ДРОССЕЛИ
О ПРИЛОЖЕНИЯХ ДИФФЕРЕНЦИАЛЬНОГО ИСЧИСЛЕНИЯ
Сложности дифференциальной диагностики фибромиалгии
ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ: ТЕОРИЯ И ПРИЛОЖЕНИЯ
Planar Linear Systems
Chaos in higher dimensional systems
Phase Portraits for Planar Systems
Nesterov acceleration for the Wasserstein minimization of displacement-convex free energies
Unified generalization analysis for physics informed neural networks
Forward and inverse problems for a time-fractional pseudo-parabolic equation with variable coefficients
Galerkin Approximation of the Fractional Sobolev Constant
Solutions of stochastic differential equations and fractal trajectories
Systems of Differential Equations
Front Matter
Tamed Feynman-Kac diffusion processes: Killing-branching intertwine
Hamiltonian formulation of the supersymmetric KdV equation
Multi-place shifted nonlocal reductions of a multi-component AKNS system
On the Darboux-Halphen system: Jacobi vs Lie
Differential Equations, Dynamical Systems, and an Introduction to Chaos
INTRODUCING DIFFERENTIAL EQUATIONS
Copyright
Preface
Lax-Oleinik formula for nonautonomous Hamilton-Jacobi equations on networks
Uniqueness of synchronized stationary equilibria in the Kuramoto mean field game
Finite-time blow-up in an elementary model of the 3D Navier-Stokes equations
Energy identity for stationary biharmonic mappings into spheres in supercritical dimensions
Dynamical chaos in two-dimensional nonlinear nonautonomous systems of ordinary differential equations
Homoclinic Phenomena
Higher-Dimensional Linear Systems
Equilibria in Nonlinear Systems
Studying discrete dynamical systems through differential equations
Ordinary Differential Equations and Dynamical Systems
Index
Ordinary Differential Equations–Dynamical Systems
Ultracontractivity of Heat semigroups in $\mathrm{L}^{2}\left( Ω\right)$ with non-local Robin boundary conditions using Nash's inequality
Solving the Sylvester equation in Banach modules
Classification of solutions to the singular Liouville's equation associated with the $N$ Finsler Laplacian
Hardy spaces and quasiregular mappings: averaged derivatives and the $\mathbb{BMO}$ case