Modulational instability in nonlinear nonlocal equations of regularized long wave type

Vera Mikyoung Hur, Ashish Kumar Pandey

Research output: Contribution to journalArticlepeer-review

Abstract

We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of Benjamin-Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations.

Original languageEnglish (US)
Pages (from-to)98-112
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume325
DOIs
StatePublished - Jun 15 2016

Keywords

  • BBM
  • Boussinesq
  • Fractional dispersion
  • Modulational instability
  • Nonlinear nonlocal
  • Regularized long wave

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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