Description of two soliton collision for the quartic gKdV equation

Yvan Martel (1) , Frank Merle (2, 3)

1 LMV - Laboratoire de Mathématiques de Versailles
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
3 IHES - Institut des Hautes Études Scientifiques

This paper concerns the problem of collision of two solitons for the quartic generalized Korteweg-de Vries equation. We introduce a new framework to describe the collision in the special case where one soliton is small with respect to the other. We prove that the two soliton survive the collision, we describe the collision phenomenon (computation of the first order of the resulting shifts on the solitons). Moreover, we prove that in this situation, there does not exist pure two-soliton solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Yvan Martel, Frank Merle. Description of two soliton collision for the quartic gKdV equation. 2007. ⟨hal-00690291⟩