Уравнения, содержащие неизвестные функции и их производные, методы их решения и приложения.


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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