General soliton solutions to a coupled Fokas-Lenells equation

2016/11/30 by Liming Ling, Bao‐Feng Feng, Ling, Liming +3 · 2 citations
Mathematics · Physics and Astronomy · #35Q58 #39A10 #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.1611.10057

openalex publication_date 2016/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• On a novel integrable generalization of the nonlinear Schrödinger equation

Cited by

• A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation
• Mechanism of State Transitions for the Vector Kuznetsov-Ma Breathers

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