General soliton solutions to a coupled Fokas–Lenells equation

• Published in: Nonlinear analysis: real world applications 2018-04, Vol.40, p.185-214
• Main Authors: Ling, Liming, Feng, Bao-Feng, Zhu, Zuonong
• Format: Article
• Language: English
• Subjects: Bright–dark soliton; Conservation laws; Coupled Fokas–Lenells equation; Dark–anti-dark soliton; Generalized Darboux transformation; Multi-Hamiltonian structure; Studies; Tu scheme
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2017.08.013

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. •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.