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We describe some recent results concerning the nonlinear -stability of multi-solitons of the Korteweg-de Vries equation [], and -stability of multi-kinks of the modified Korteweg-de Vries []. 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 [, ].
The aim of this note is to give a short review of our recent work (see []) with Miguel A. Alejo and Luis Vega, concerning the -stability, and asymptotic stability, of the - of the Korteweg-de Vries (KdV) equation.
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