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].

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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