Description of two soliton collision for the quartic gKdV equation

TL;DR

This paper investigates the collision of two solitons in the quartic gKdV equation, introducing a new framework for analysis when one soliton is small, and demonstrating their survival post-collision with specific shift computations.

Contribution

It presents a novel analytical framework for soliton collisions in the quartic gKdV equation, especially when one soliton is significantly smaller.

Findings

Two solitons survive the collision.

Computed the first-order shifts resulting from the collision.

Proved the non-existence of pure two-soliton solutions in this scenario.

Abstract

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.