On the nonlinear stability of mKdV breathers

Miguel Á. Alejo, Claudio Muñoz

Type: Article

Publication Date: 2012-10-12

Citations: 27

DOI: https://doi.org/10.1088/1751-8113/45/43/432001

Abstract

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

Locations

arXiv (Cornell University) - View - PDF
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Journal of Physics A Mathematical and Theoretical - View

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+ PDF Chat	Breather lattice and its stabilization for the modified Korteweg–de Vries equation	2003	P. G. Kevrekidis Avinash Khare Avadh Saxena
+	Instability of solitons for the critical generalized Korteweg—de Vries equation	2001	Yvan Martel Franck Merle
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