Orbits homoclinic to centre manifolds of conservative PDEs

Jalal Shatah, Chongchun Zeng

Research output: Contribution to journalArticle

Abstract

In this paper, perturbations to orbits homoclinic to saddle-centres for conservative systems are considered. We prove that if the Hessian of the conserved energy at the saddle-centre is positive definite in the centre directions, then either single bump orbits homoclinic to the saddle-centre persist or its centre-unstable and centre-stable manifolds intersect transversally, where the centre manifold is stable. The return map induced by the homoclinic orbits to the centre manifold and applications to sine-Gordon breathers, homoclinic orbits for nonlinear Schrödinger equations, and periodic travelling waves for Klein-Gordon equations are discussed.

Original languageEnglish (US)
Pages (from-to)591-614
Number of pages24
JournalNonlinearity
Volume16
Issue number2
DOIs
StatePublished - Mar 1 2003

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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