General soliton solutions to a coupled Fokas–Lenells equation. (April 2018) - Ling, Liming; Feng, Bao-Feng; Zhu, Zuonong
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. Highlights: We construct a generalized Darboux transformation (gDT) to a coupled Fokas–Lenells (FL) equation. We construct multi-Hamiltonian structure and infinitely many conservation laws to the coupled FL equation. Multi-bright soliton solution to the coupled FL equation is constructed based on the gDT. A variety of single soliton solutions with nonzero boundary condition are constructed and classified. Multi-dark soliton solution to the coupled FL equation is constructed by the limit technique.