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Chin. Phys. B, 2018, Vol. 27(7): 070201    DOI: 10.1088/1674-1056/27/7/070201
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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
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.
Keywords:  coupled modified nonlinear Schrödinger equations      Riemann-Hilbert approach      multi-soliton solutions  
Received:  30 January 2018      Revised:  20 April 2018      Published:  05 July 2018
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).
Corresponding Authors:  Tie-Cheng Xia     E-mail:  xiatc@shu.edu.cn

Cite this article: 

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 2018 Chin. Phys. B 27 070201

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