On soliton structure of the Vakhnenko equation with a 'dissipative' term: a peculiar fission phenomenon

TL;DR

This paper explores the soliton solutions of the Vakhnenko equation with dissipation, revealing three types of solitons and a unique fission scattering phenomenon using Hirota's method.

Contribution

It introduces a new classification of soliton solutions for the dissipative Vakhnenko equation and uncovers a novel fission scattering behavior.

Findings

Three types of soliton solutions identified

Fission phenomenon observed in soliton scattering

Dependence of solutions on dissipation parameter

Abstract

In the present work, we investigate the soliton structure of the Vakhnenko equation with a 'dissipative' term, by means of the Hirota's method. As a result, we unearth three kinds of soliton solutions depending upon the dissipation parameter. We further find that the scattering behavior among such structures exhibits a peculiar feature that may be the fission phenomenon.