Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis

N. M. Ercolani, D. W. McLaughlin, H. Roitner

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

In this paper we rigorously show the existence and smoothness in ε of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameter ε. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.

Original languageEnglish (US)
Pages (from-to)477-539
Number of pages63
JournalJournal of Nonlinear Science
Volume3
Issue number1
DOIs
StatePublished - Dec 1 1993

Keywords

  • attractors
  • nearly integrable systems
  • numerical methods
  • spectral transform
  • stability
  • traveling waves

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

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