On the nonlinear stability of mKdV breathers
Analysis of PDEs
2015-06-05 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1206.3151,
title = {On the nonlinear stability of mKdV breathers},
author = {Miguel Angel Alejo and Claudio Muñoz},
journal= {arXiv preprint arXiv:1206.3151},
year = {2015}
}
Comments
7 pp