Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations

Vera Mikyoung Hur; Mathew A. Johnson

Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations

Analysis of PDEs 2015-01-13 v3

Authors: Vera Mikyoung Hur , Mathew A. Johnson

Abstract

We consider the stability and instability of periodic travling waves for Korteweg-de Vries type equations with fractional dispersion and other nonlinear dispersive equations. We establish that a constrained minimizer for the related variational problem is nonlinearly stable to period preserving perturbations. We also discuss when the associated linearized equation admits exponentially growing solutions. The proof utilizes the variational structure of the equation.

Keywords

periodic traveling waves stability nonlinear dispersive equations Korteweg-de Vries equation variational structure constrained minimizer

Cite

@article{arxiv.1303.4765,
  title  = {Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations},
  author = {Vera Mikyoung Hur and Mathew A. Johnson},
  journal= {arXiv preprint arXiv:1303.4765},
  year   = {2015}
}

Comments

27 pages. Missing assumption added to stability theorem. arXiv admin note: text overlap with arXiv:1303.2605

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