On the nonlinear stability of mKdV breathers
Miguel Angel Alejo, Claudio Mu\~noz
TL;DR
This paper provides a rigorous mathematical proof of the nonlinear stability of mKdV breathers using a novel Lyapunov functional and specialized analytical techniques in the energy space.
Contribution
It introduces a new Lyapunov functional and a nonlinear equation framework to establish the stability of mKdV breathers, advancing understanding in nonlinear wave stability.
Findings
Proof of nonlinear stability of mKdV breathers
Development of a new Lyapunov functional in the energy space
Insights into stability in the sine-Gordon case
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.
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