Inelastically generated solitons and anti-solitons in the perturbed KdV equation

TL;DR

This paper investigates how common perturbations affect the multi-soliton solutions of the KdV equation, revealing the emergence of inelastic soliton-anti-soliton waves that evolve along characteristic lines.

Contribution

It introduces a detailed analysis of inelastic components in perturbed KdV solitons, highlighting the generation of soliton-anti-soliton waves and their asymptotic behavior.

Findings

Elastic component preserves soliton scattering picture.

Inelastic component generates soliton-anti-soliton waves.

Inelastic waves asymptote into solitons and anti-solitons.

Abstract

Under the effect of common perturbations, the multiple-soliton solution of the KdV equation is transformed into a sum of an elastic and a first-order inelastic component. The elastic component is a perturbation series, identical in structure to the perturbed single-soliton solution. It preserves the soliton-scattering picture. The inelastic component is generated by perturbation terms that represent coupling between KdV solitons and inelastically generated soliton-anti-soliton waves. It asymptotes into solitons and anti-solitons, that evolve along the characteristic lines of the KdV solitons. This is demonstrated in the two-soliton case.