Stability of two soliton collision for nonintegrable gKdV equations

TL;DR

This paper investigates the stability and collision dynamics of two solitons in nonintegrable gKdV equations, extending previous work to more general nonlinearities and demonstrating soliton survival during collisions.

Contribution

It generalizes the analysis of two-soliton collisions to a broader class of gKdV equations with nonlinear stability, providing detailed collision descriptions.

Findings

Two solitons survive collisions in nonintegrable gKdV equations.

The collision behavior is characterized at the main order.

The framework applies to general nonlinearities with stable solitons.

Abstract

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.