Nonlinear Stability of MKdV Breathers
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Nonlinear Stability of MKdV Breathers. / Alejo Plana, Miguel Angel; Muñoz, Claudio .
I: Communications in Mathematical Physics, Bind 34, Nr. 1, 2013, s. 233-262.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Nonlinear Stability of MKdV Breathers
AU - Alejo Plana, Miguel Angel
AU - Muñoz, Claudio
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.1007/s00220-013-1792-0
DO - 10.1007/s00220-013-1792-0
M3 - Journal article
VL - 34
SP - 233
EP - 262
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -
ID: 113813696