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 2003

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pulse detonation engines
Center Manifold
Homoclinic Orbit
Orbits
Saddle
orbits
saddles
Periodic Traveling Waves
Return Map
Conservative System
Stable Manifold
Breathers
Klein-Gordon Equation
Intersect
Nonlinear equations
Positive definite
Nonlinear Equations
Unstable
Perturbation
Klein-Gordon equation

ASJC Scopus subject areas

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

Cite this

Orbits homoclinic to centre manifolds of conservative PDEs. / Shatah, Jalal; Zeng, Chongchun.

In: Nonlinearity, Vol. 16, No. 2, 03.2003, p. 591-614.

Research output: Contribution to journalArticle

Shatah, Jalal ; Zeng, Chongchun. / Orbits homoclinic to centre manifolds of conservative PDEs. In: Nonlinearity. 2003 ; Vol. 16, No. 2. pp. 591-614.
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