A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS
From MaRDI portal
Publication:3498689
DOI10.1142/S0218127406016471zbMath1143.35373MaRDI QIDQ3498689
Publication date: 16 May 2008
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory (37-01) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Homoclinic and heteroclinic orbits for dynamical systems (37C29)
Related Items (2)
Global dynamics of a pipe conveying pulsating fluid in primary parametrical resonance: analytical and numerical results from the nonlinear wave equation ⋮ Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Persistent homoclinic orbits for nonlinear Schrödinger equation under singular perturbations
- Existence of chaos for nonlinear Schrödinger equation under singular perturbations
- Equilibria, connecting orbits and a priori bounds for semilinear parabolic equations with nonlinear boundary conditions
- Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
- Geometry of the modulational instability. III: Homoclinic orbits for the periodic sine-Gordon equation
- Gauge theory of Bäcklund transformations. II
- A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
- Smale horseshoes and symbolic dynamics in perturbed nonlinear Schrödinger equations
- Darboux coordinates and Liouville-Arnold integration in loop algebras
- Homoclinics: Poincaré-Melnikov type results via a variational approach
- Homoclinic orbits for soliton equations solvable via the quadratic bundle
- Chaos and shadowing lemma for autonomous systems of infinite dimensions
- Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDE's
- On the Bäcklund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system
- Bäcklund-Darboux transformations and Melnikov analysis for Davey-Stewartson II equations
- Homoclinic connections of unstable plane waves of the modified nonlinear Schrödinger equation
- Chaos for a damped and forced KdV equation
- Chaos in driven Alfvén systems: boundary and interior crises
- Mel'nikov analysis of numerically induced chaos in the nonlinear Schrödinger equation
- Spatial chaos in weakly dispersive and viscous media: A nonperturbative theory of the driven KdV-Burgers equation
- Chaotic dynamics of an unstable Burgers equation
- Modified Manakov system with self-consistent source.
- Homoclinic orbits for the coupled nonlinear Schrödinger system and long-short wave equation
- Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows
- Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas
- On Homoclinic Structure and Numerically Induced Chaos for the Nonlinear Schrödinger Equation
- Transverse homoclinic orbits in periodically perturbed parabolic equations
- Painleve analysis of the non-linear Schrodinger family of equations
- The sine-gordon and sinh-gordon equations on the circle
- Spectral theory for the periodic sine-Gordon equation: A concrete viewpoint
- Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- Homoclinic orbits for the perturbed sine-Gordon equation
- A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM
- ALFVÉN BOUNDARY CRISIS
- CHAOS IN A NEAR-INTEGRABLE HAMILTONIAN LATTICE
- Singularly Perturbed Vector and Scalar Nonlinear Schrödinger Equations with Persistent Homoclinic Orbits
- Bounded solutions for non-autonomous parabolic equations
- Existence of homoclinic tubes in the sine-Gordon equation with Hamiltonian perturbation
- Integrals of nonlinear equations of evolution and solitary waves
- Invariant manifolds
- Spatiotemporal chaos in spatially extended systems
This page was built for publication: A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS
