Persistent homoclinic orbits for a perturbed nonlinear Schrödinger equation

Y. Li; David W. McLaughlin; Jalal Shatah; S. Wiggins

doi:10.1002/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9

Persistent homoclinic orbits for a perturbed nonlinear Schrödinger equation

Y. Li
, David W. McLaughlin
, Jalal Shatah
, S. Wiggins

Research output: Contribution to journal › Article › peer-review

85 Scopus citations

Abstract

The persistence of homoclinic orbits for certain perturbations of the integrable nonlinear Schrödinger equation under even periodic boundary conditions is established. More specifically, the existence of a symmetric pair of homoclinic orbits is established for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE.

Original language	English
Pages (from-to)	1175-1255
Number of pages	81
Journal	Communications on Pure and Applied Mathematics
Volume	49
Issue number	11
DOIs	https://doi.org/10.1002/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9
State	Published - Nov 1996
Externally published	Yes

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10.1002/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9

Cite this

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title = "Persistent homoclinic orbits for a perturbed nonlinear Schr{\"o}dinger equation",

abstract = "The persistence of homoclinic orbits for certain perturbations of the integrable nonlinear Schr{\"o}dinger equation under even periodic boundary conditions is established. More specifically, the existence of a symmetric pair of homoclinic orbits is established for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE.",

author = "Y. Li and McLaughlin, \{David W.\} and Jalal Shatah and S. Wiggins",

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AU - Li, Y.

AU - McLaughlin, David W.

AU - Shatah, Jalal

AU - Wiggins, S.

PY - 1996/11

Y1 - 1996/11

N2 - The persistence of homoclinic orbits for certain perturbations of the integrable nonlinear Schrödinger equation under even periodic boundary conditions is established. More specifically, the existence of a symmetric pair of homoclinic orbits is established for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE.

AB - The persistence of homoclinic orbits for certain perturbations of the integrable nonlinear Schrödinger equation under even periodic boundary conditions is established. More specifically, the existence of a symmetric pair of homoclinic orbits is established for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE.

UR - https://www.scopus.com/pages/publications/0030506927

U2 - 10.1002/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9

DO - 10.1002/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9

M3 - Article

AN - SCOPUS:0030506927

SN - 0010-3640

VL - 49

SP - 1175

EP - 1255

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 11

ER -

Persistent homoclinic orbits for a perturbed nonlinear Schrödinger equation

Abstract

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