Numerical computation of soliton dynamics for NLS equations in a driving potential.

Caliari, Marco; Squassina, Marco

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We describe some recent results concerning the nonlinear $L^{2}$ -stability of multi-solitons of the Korteweg-de Vries equation [], and $H^{1}$ -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 [, ].