The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift

被引：46

作者：

Zou, Zhifu ^{[1
]}

Guo, Rui ^{[1
]}

机构：

[1] Taiyuan Univ Technol, Sch Math, Taiyuan 030024, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2023年 / 124卷

基金：

中国国家自然科学基金;

关键词：

The higher-order Gerdjikov-Ivanov; equation; Inverse scattering transformation; Riemann-Hilbert method; Soliton solutions; Position shift; INVERSE SCATTERING TRANSFORM; NONLINEAR SCHRODINGER-EQUATION; LONG-TIME ASYMPTOTICS; EVOLUTION-EQUATIONS; MANAKOV SYSTEM;

D O I：

10.1016/j.cnsns.2023.107316

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation with nonzero boundary conditions. A uniformization variable will be introduced to make it forms a one-to-one mapping with the spectral parameter. The analyticity, symmetric and asymptotic behaviors of the eigenfunctions and scattering datas will be calculated in detail and the Riemann-Hilbert problem will be constructed to obtain the expression for the N-soliton solutions. In addition, the case of Jost solutions and scattering coefficients near the branch points will also be analyzed. On the other hand, when the boundary conditions turn to zero, the formula for the position shifts and phase shifts of solitons resulting from soliton interactions will be solved.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：23

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