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

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

Research output: Contribution to journalArticle

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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
Publication statusPublished - Dec 1993

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Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Applied Mathematics
  • Mathematics(all)
  • Mechanics of Materials
  • Computational Mechanics

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