Singularly Perturbed Vector and Scalar Nonlinear Schrödinger Equations with Persistent Homoclinic Orbits

DOI10.1111/1467-9590.00002zbMath1152.35496arXivmath/0205113OpenAlexW2005452358MaRDI QIDQ4784772

Y. Charles Li

Publication date: 11 December 2002

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0205113

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Infinite-dimensional dissipative dynamical systems (37L99)

Related Items (11)

Global dynamics of a pipe conveying pulsating fluid in primary parametrical resonance: analytical and numerical results from the nonlinear wave equation ⋮ General N-Dark-Dark Solitons in the Coupled Nonlinear Schrödinger Equations ⋮ Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate ⋮ A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS ⋮ Existence of chaos in evolution equations ⋮ Chaos in Miles' equations ⋮ Homoclinic orbits for perturbed coupled nonlinear Schrödinger equations ⋮ Homoclinic orbits for coupled modified nonlinear Schrödinger equations ⋮ Dressing procedure for some homoclinic connections of the Manakov system ⋮ First Order Approximation of an Elliptic 3D Singular Perturbation Problem ⋮ First Order Approximation of an Elliptic 3D Singular Perturbation Problem

Cites Work

• Unnamed Item
• Unnamed Item
• On integrability and chaos in discrete systems
• On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems
• Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDE's
• Bäcklund-Darboux transformations and Melnikov analysis for Davey-Stewartson II equations
• Fractal dependence of vector-soliton collisions in birefringent fibers
• On discretizations of the vector nonlinear Schrödinger equation

This page was built for publication: Singularly Perturbed Vector and Scalar Nonlinear Schrödinger Equations with Persistent Homoclinic Orbits