General soliton solutions to a coupled Fokas–Lenells equation

Abstract

In this paper, we firstly establish the multi-Hamiltonian structure and infinitely 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.