${H}^{1}$-stability of mKdV multi-kinks
Journées équations aux dérivées partielles (2011), article no. 8, 16 p.

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].

DOI : https://doi.org/10.5802/jedp.80
Keywords: KdV equation, modified KdV equation, Gardner equation, integrability, multi-soliton, multi-kink, stability, asymptotic stability, Gardner transform
@article{JEDP_2011____A8_0,
author = {Mu\~noz, Claudio},
title = {$H^1$-stability of mKdV multi-kinks},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2011},
doi = {10.5802/jedp.80},
language = {en},
url = {http://www.numdam.org/item/JEDP_2011____A8_0}
}

Muñoz, Claudio. $H^1$-stability of mKdV multi-kinks. Journées équations aux dérivées partielles (2011), article  no. 8, 16 p. doi : 10.5802/jedp.80. http://www.numdam.org/item/JEDP_2011____A8_0/

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