Journal of Nonlinear Mathematical Physics

Volume 28, Issue 1, March 2021, Pages 38 - 52

Inverse Scattering Transformation for the Fokas–Lenells Equation with Nonzero Boundary Conditions

Authors
Yi Zhao, Engui Fan*
School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China
*Corresponding author. Email: faneg@fudan.edu.cn
Corresponding Author
Engui Fan
Received 12 February 2020, Accepted 3 March 2020, Available Online 10 December 2020.
DOI
https://doi.org/10.2991/jnmp.k.200922.003How to use a DOI?
Keywords
Fokas–Lenells equation, nonzero boundary conditions, inverse scattering transformation, Riemann–Hilbert problem, N-soliton solution
Abstract

In this article, we focus on the inverse scattering transformation for the Fokas–Lenells (FL) equation with nonzero boundary conditions via the Riemann–Hilbert (RH) approach. Based on the Lax pair of the FL equation, the analyticity, symmetry and asymptotic behavior of the Jost solutions and scattering matrix are discussed in detail. With these results, we further present a generalized RH problem, from which a reconstruction formula between the solution of the FL equation and the Riemann–Hilbert problem is obtained. The N-soliton solutions of the FL equation is obtained by solving the RH problem.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 1
Pages
38 - 52
Publication Date
2020/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.k.200922.003How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Yi Zhao
AU  - Engui Fan
PY  - 2020
DA  - 2020/12
TI  - Inverse Scattering Transformation for the Fokas–Lenells Equation with Nonzero Boundary Conditions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 38
EP  - 52
VL  - 28
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.200922.003
DO  - https://doi.org/10.2991/jnmp.k.200922.003
ID  - Zhao2020
ER  -