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

被引：24

作者：

Zhao, Yi ^{[1
]}

Fan, Engui ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2021年 / 28卷 / 01期

基金：

美国国家科学基金会;

关键词：

Fokas-Lenells equation; nonzero boundary conditions; inverse scattering transformation; Riemann-Hilbert problem; N-soliton solution;

D O I：

10.2991/jnmp.k.200922.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2020 The Authors. Published by Atlantis Press B.V.

引用

页码：38 / 52

页数：15

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