General soliton solutions to a coupled Fokas–Lenells equation. (April 2018)

• Record Type: Journal Article
• Authors: Ling, Liming; Feng, Bao-Feng; Zhu, Zuonong
• Is Part Of: Nonlinear analysis. Volume 40(2018)
• Page Start: 185
• Page End: 214
• Publication Date: 2018-04
• Subjects: Coupled Fokas–Lenells equation -- Tu scheme -- Multi-Hamiltonian structure -- Generalized Darboux transformation -- Bright–dark soliton -- Dark–anti-dark soliton; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.08.013
• Languages: English
• ISSNs: 1468-1218

Abstract

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.