Riemann-Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrodinger equations

被引：110

作者：

Peng, Wei-Qi ^{[1
,2
]}

Tian, Shou-Fu ^{[1
,2
]}

Wang, Xiu-Bin ^{[4
]}

Zhang, Tian-Tian ^{[1
,2
]}

Fang, Yong ^{[3
]}

机构：

[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China

[2] China Univ Min & Technol, Inst Math Phys, Xuzhou 221116, Jiangsu, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[4] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 146卷

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Three-component coupled nonlinear; Schrodinger equation; Riemann-Hilbert formulation; Multi-soliton solutions; Dynamic behaviors; N-SOLITON SOLUTIONS;

D O I：

10.1016/j.geomphys.2019.103508

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An integrable three-component coupled nonlinear Schrodinger (NLS) equation is considered in this work. We present the scattering and inverse scattering problems of the three-component coupled NLS equation by using the Riemann-Hilbert formulation. Furthermore, according to the Riemann-Hilbert method, the multi-soliton solutions of this equation are derived. We also analyze the collision dynamic behaviors of these solitons. Moreover, a new phenomenon for two-soliton collision is displayed, which is unique and not common in integrable systems. It is hoped that our results can help enrich the nonlinear dynamics of the NLS-type equations. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：9

共 22 条

[1]

Ablowitz MJ, 1991, Nonlinear Evolution Equations and Inverse Scattering

[2]

Bluman G.W., 2013, Symmetries and differential equations, V81

[3] Riemann-Hilbert approach and N-soliton solutions for a generalized Sasa-Satsuma equation [J].

Geng, Xianguo ;

Wu, Jianping .

WAVE MOTION, 2016, 60 :62-72

[4] Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrodinger equation [J].

Guo, Boling ;

Ling, Liming .

JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (07)

[5]

Hirota R., 2004, DIRECT METHODS SOLIT

[6] The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation [J].

Ma, Wen-Xiu .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 471 (1-2) :796-811

[7] Riemann-Hilbert problems and N-soliton solutions for a coupled mKdV system [J].

Ma, Wen-Xiu .

JOURNAL OF GEOMETRY AND PHYSICS, 2018, 132 :45-54

[8]

Matveev V.B., 1991, Darboux Transformations and Solitons

[9] LONG-TIME ASYMPTOTIC BEHAVIOR FOR THE GERDJIKOV-IVANOV TYPE OF DERIVATIVE NONLINEAR SCHRODINGER EQUATION WITH TIME-PERIODIC BOUNDARY CONDITION [J].

Tian, Shou-Fu ;

Zhang, Tian-Tian .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (04) :1713-1729

[10] The mixed coupled nonlinear Schrodinger equation on the half-line via the Fokas method [J].

Tian, Shou-Fu .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2016, 472 (2195)

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