Stability of two soliton collision for nonintegrable gKdV equations

Details Stability of two soliton collision for nonintegrable gKdV equations Stability of two soliton collision for nonintegrable gKdV equations

2007-09-17

arxiv.org/abs/0709.2677v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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