Stability of periodic traveling waves for nonlinear dispersive equations

Vera Mikyoung Hur, Mathew A. Johnson

Research output: Contribution to journalArticlepeer-review


We study the stability and instability of periodic traveling waves for Korteweg-de Vries-type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations, provided that the associated linearized operator enjoys a Jordan block structure. We then discuss when the linearized equation admits solutions exponentially growing in time.

Original languageEnglish (US)
Pages (from-to)3528-3554
Number of pages27
JournalSIAM Journal on Mathematical Analysis
Issue number5
StatePublished - 2015


  • Nonlinear dispersive
  • Nonlocal
  • Periodic traveling waves
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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