Inverse Scattering Transformation for the Fokas–Lenells Equation with Nonzero Boundary Conditions
- 10.2991/jnmp.k.200922.003How to use a DOI?
- Fokas–Lenells equation; nonzero boundary conditions; inverse scattering transformation; Riemann–Hilbert problem; N-soliton solution
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.
- © 2020 The Authors. Published by Atlantis Press B.V.
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- 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 - 2020/12/10 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 -