Stability of two soliton collision for nonintegrable gKdV equations

Understand

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.