Nonlinear dynamics of solitons for the vector modified Korteweg-de Vries equation

TL;DR

This paper develops the inverse scattering transform for a vector modified Korteweg-de Vries equation, constructs soliton and breather solutions, and studies their collision dynamics, revealing multi-component structures.

Contribution

It introduces a vector generalization of the mKdV equation, providing a new integrable model and explicit multi-component soliton solutions.

Findings

Existence of multi-component soliton solutions.

Construction of breather solutions.

Analysis of soliton collision processes.

Abstract

We consider the vector generalization of the modified Korteweg-de Vries equation. We develop the inverse scattering transform for solving this equation. We construct the solitons and the breather solutions and investigate the processes of their collisions. We show that along with one-component soliton solutions, there are solutions which have essentially three-component structure.