Nonlinear Stability of MKdV Breathers

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

  • Miguel Angel Alejo Plana
  • 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.
OriginalsprogEngelsk
TidsskriftCommunications in Mathematical Physics
Vol/bind34
Udgave nummer1
Sider (fra-til)233-262
ISSN0010-3616
DOI
StatusUdgivet - 2013

ID: 113813696