Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach

doi:10.1088/1674-1056/27/7/070201

中国物理B ›› 2018, Vol. 27 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/27/7/070201

• GENERAL • 下一篇

Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach

Zhou-Zheng Kang(康周正), Tie-Cheng Xia(夏铁成), Xi Ma(马茜)

1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
2 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China

收稿日期:2018-01-30 修回日期:2018-04-20 出版日期:2018-07-05 发布日期:2018-07-05
通讯作者: Tie-Cheng Xia E-mail:xiatc@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach

Zhou-Zheng Kang(康周正)^1,2, Tie-Cheng Xia(夏铁成)¹, Xi Ma(马茜)¹

1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
2 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China

Received:2018-01-30 Revised:2018-04-20 Online:2018-07-05 Published:2018-07-05
Contact: Tie-Cheng Xia E-mail:xiatc@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

摘要/Abstract

摘要： The coupled modified nonlinear Schrödinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrödinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.

关键词: coupled modified nonlinear Schrödinger equations, Riemann-Hilbert approach, multi-soliton solutions

Abstract: The coupled modified nonlinear Schrödinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrödinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.

Key words: coupled modified nonlinear Schrödinger equations, Riemann-Hilbert approach, multi-soliton solutions

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems) 05.45.Yv (Solitons)

康周正, 夏铁成, 马茜. Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach[J]. 中国物理B, 2018, 27(7): 70201-070201.

Zhou-Zheng Kang(康周正), Tie-Cheng Xia(夏铁成), Xi Ma(马茜). Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach[J]. Chin. Phys. B, 2018, 27(7): 70201-070201.

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Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach

Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach

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