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Claudio Muñoz
$H^1$-stability of mKdV multi-kinks
Journées équations aux dérivées partielles (2011), Exp. No. 8, 16 p., doi: 10.5802/jedp.80
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Mots clés: KdV equation, modified KdV equation, Gardner equation, integrability, multi-soliton, multi-kink, stability, asymptotic stability, Gardner transform

Résumé - Abstract

We describe some recent results concerning the nonlinear $L^2$-stability of multi-solitons of the Korteweg-de Vries equation [4], and $H^1$-stability of multi-kinks of the modified Korteweg-de Vries [49]. The proof of both results is closely linked to stability properties for solitons of the integrable Gardner equation, which have been considered by Martel, Merle and Tsai [41, 40].

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