Inelastic soliton processes generated by the perturbed KdV equation

TL;DR

This paper investigates how perturbations to the KdV equation induce inelastic interactions among solitons, leading to the emergence of new wave phenomena such as soliton creation, annihilation, and scattering.

Contribution

It introduces a detailed analysis of inelastic soliton interactions caused by perturbations in the KdV equation, highlighting the formation of new waves in the first-order correction.

Findings

Perturbations lead to inelastic interactions among KdV solitons.

New waves include soliton-anti-soliton creation and annihilation.

First-order corrections reveal complex wave phenomena.

Abstract

Perturbations commonly added to the KdV equation contain terms that represent inelastic interac-tions among KdV solitons in multiple-soliton solutions. These terms trigger the emergence of new waves in the first-order correction to the solution of the perturbed equation. The new waves can represent soliton-anti-soliton creation, annihilation and scattering. Other possible waves represent soliton decay and production.