Stability of two soliton collision for nonintegrable gKdV equations

Yvan Martel (1) , Frank Merle (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We continue our study of the collision of two solitons for the subcritical generalized KdV equations. In a previous paper, mainly devoted to the case of the quartic gKdV equation, we have introduced a new framework to understand the collision of two solitons in the case where one soliton is small with respect to the other. In this paper, we consider the case of a general nonlinearity $f(u)$ for which the two solitons are nonlinearly stable. We prove that in this situation the two solitons survive and we describe the collision at the main orders.

Domaines: Equations aux dérivées partielles [math.AP]

Yvan Martel, Frank Merle. Stability of two soliton collision for nonintegrable gKdV equations. Communications in Mathematical Physics, 2009, 286, pp.39-79. ⟨hal-00408108⟩