General soliton solutions to a coupled Fokas-Lenells equation

TL;DR

This paper develops a comprehensive framework for soliton solutions to a coupled Fokas-Lenells equation, including multi-soliton solutions and their behaviors, based on Hamiltonian structures and Darboux transformations.

Contribution

It introduces a generalized Darboux transformation for the coupled Fokas-Lenells equation and constructs various explicit soliton solutions.

Findings

Derived explicit one-soliton solutions including bright-dark and breather-like types

Constructed multi-soliton solutions and analyzed their asymptotic behaviors

Established Hamiltonian structures and conservation laws for the hierarchy

Abstract

In this paper, we firstly establish the multi-Hamiltonian structure and infinite many conservation laws for the vector Kaup-Newell hierarchy of the positive and negative orders. The first nontrivial negative flow corresponds to a coupled Fokas-Lenells equation. By constructing a generalized Darboux transformation and using a limiting process, all kinds of one-soliton solutions are constructed including the bright-dark soliton, the dark-anti-dark soliton and the breather-like solutions. Furthermore, multi-bright and multi-dark soliton solutions are derived and their asymptotic behaviors are investigated.