Orbital stability of one-parameter periodic traveling waves for dispersive equations and applications

Abstract

This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas. As a consequence of our result, we give several applications for well known dispersive equations. Extension of the theory to regularized equations is also established.

31 pages, 12 figures

References in corpus (1)

• The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation

Cited by in corpus (1)

• Global well-posedness for $H^{-1}(\mathbb{R})$ perturbations of KdV with exotic spatial asymptotics