Friday, June 15, 2012

1206.3157 (Miguel Angel Alejo et al.)

Nonlinear stability of mKdV breathers    [PDF]

Miguel Angel Alejo, Claudio Muñoz
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H^2 topology. Our proof introduces a new Lyapunov functional, at the H^2 level, which allows to describe the dynamics of small perturbations, including oscillations induced by the periodicity of the solution, as well as a direct control of the corresponding instability modes. In particular, degenerate directions are controlled using low-regularity conservation laws.
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