Inelastic interaction of nearly equal solitons for the quartic gKdV equation

TL;DR

This paper analyzes the interaction of nearly equal solitons in the quartic gKdV equation, showing they largely preserve their shape but experience inelastic collisions, unlike in integrable cases.

Contribution

It provides a complete description of soliton interactions for the quartic gKdV, highlighting non-elastic collisions in a non-integrable setting.

Findings

Solitons are preserved at main order during interaction.

Solitons remain separated by large distances over time.

Collisions are inelastic, unlike in integrable equations.

Abstract

This paper presents a complete description of the interaction of two solitons with nearly equal speeds for the quartic (gKdV) equation. By constructing an approximate solution of the problem, we prove that at the main order, the two solitons are preserved by the interaction and that for all time they are separated by a large distance, as in the case of the integrable KdV equation in this regime. However, unlike in the integrable case, we prove that the collision is not perfectly elastic.