Mixed interactions of localized waves in the three-component coupled derivative nonlinear Schr\"{o}dinger equations

TL;DR

This paper constructs Darboux transformations for three-component coupled derivative nonlinear Schrödinger equations, classifies various higher-order localized wave interactions, and analyzes how parameters influence wave dynamics.

Contribution

It introduces a complete classification of interactional solutions among rogue waves, solitons, and breathers in a three-component system, highlighting the role of free parameters.

Findings

Six types of interactional solutions classified

Four mixed localized wave interactions identified

Parameters significantly affect wave merging and dynamics

Abstract

The Darboux transformation of the three-component coupled derivative nonlinear Schr\"{o}dinger equations is constructed, based on the special vector solution elaborately generated from the corresponding Lax pair, various interactions of localized waves are derived. Here, we focus on the higher-order interactional solutions among higher-order rogue waves (RWs), multi-soliton and multi-breather. Instead of considering various arrangements among the three components $q_1$, $q_2$ and $q_3$, we define the same combination as the same type solution. Based on our method, these interactional solutions are completely classified into six types among these three components $q_1$, $q_2$ and $q_3$. In these six types interactional solutions, there are four mixed interactions of localized waves in three different components. In particular, the free parameters $\alpha$ and $\beta$ paly an important role in dynamics structures of the interactional solutions, for example, different nonlinear localized waves merge with each other by increasing the absolute values of $\alpha$ and $\beta$.