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

DOI

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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TY  - JOUR
AU  - Yi Zhao
AU  - Engui Fan
PY  - 2020
DA  - 2020/12/10
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  - 10.2991/jnmp.k.200922.003
ID  - Zhao2020
ER  -