Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations

Abstract:We prove in this paper the asymptotic completeness of the family of solitons in the energy space for generalized Korteweg-de Vries equations in the subcritical case (this includes in particular the KdV equation and the modified KdV equation). This result is obtained as a consequence of a rigidity theorem on the flow close to a soliton up to a scaling and a translation, which has its own interest. The proofs use some tools introduced in a previous paper to prove similar results in the case of critical generalized KdV equation.

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