Abstract
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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Alejo, M.A., Muñoz, C. Nonlinear Stability of MKdV Breathers. Commun. Math. Phys. 324, 233–262 (2013). https://doi.org/10.1007/s00220-013-1792-0
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DOI: https://doi.org/10.1007/s00220-013-1792-0