Localized wave solutions of three-component defocusing Kundu-Eckhaus equation with 4x4 matrix spectral problem

TL;DR

This paper derives localized wave solutions for a three-component defocusing Kundu-Eckhaus equation using binary Darboux transformation, revealing novel breather solutions and advancing understanding of coupled nonlinear wave phenomena.

Contribution

It introduces a binary Darboux transformation approach for the three-component system and finds new breather solutions absent in single-component models.

Findings

Derived vector dark soliton solutions.

Obtained asymptotic expressions for dark solitons.

Discovered breather and Y-shaped breather solutions.

Abstract

This work focuses on three-component defocusing Kundu-Eckhaus equation, which serves as a significant coupled model for describing complex wave propagation in nonlinear optical fibers. By employing binary Darboux transformation based on 4x4 matrix spectral problem, we derive vector dark soliton solutions, and meanwhile, the exact expressions of asymptotic dark soliton components are obtained through an asymptotic analysis method. Furthermore, breather and Y-shaped breather solutions, absent from single-component defocusing kundu-Eckhaus systems, are obtained due to the mutual coupling effects between different components. The results significantly advance our understanding nonlinear wave phenomenon induced by coupling effects and provide a theoretical reference for subsequent studies on defocusing multi-component systems.