1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Mathematics, The University of Chicago, USA3 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
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.
Communications in Mathematical Physics, 2013, Vol 34, Issue 1, p. 233-262