Nonlinear Stability of MKdV Breathers
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Communications in Mathematical Physics |
Volume | 34 |
Issue number | 1 |
Pages (from-to) | 233-262 |
ISSN | 0010-3616 |
DOIs | |
Publication status | Published - 2013 |
ID: 113813696