Localized wave solutions of three-component defocusing Kundu–Eckhaus equation with \(4\times4\) matrix spectral problem

Abstract

This work focuses on the three-component defocusing Kundu–Eckhaus equation, which serves as a significant coupled model for describing complex wave propagation in nonlinear optical fibers. By employing the binary Darboux transformation based on a \(4\times4\) matrix spectral problem, we derive vector dark soliton solutions, while 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 of nonlinear wave phenomena induced by coupling effects and provide a theoretical reference for subsequent studies on defocusing multi-component systems.