2012/06/30 by Miguel Angel Alejo, Claudio Muñoz · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.AP #math.MP
paper · pdf · doi:10.1088/1751-8113/45/43/432001
7 pp
arxiv created 2012/09/29 · arxiv updated 2015/06/05
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.