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Chin. Phys. B, 2018, Vol. 27(12): 120202    DOI: 10.1088/1674-1056/27/12/120202
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N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method

Si-Qi Xu(徐思齐)1,2, Xian-Guo Geng(耿献国)1
1 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2 College of Civil Engineering, Xinyang Normal University, Xinyang 464000, China
Abstract  

In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann-Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann-Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann-Hilbert problem in both the regular and non-regular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover, the dynamical behaviour of the single-soliton solution is shown graphically.

Keywords:  nonlocal two-wave interaction system      Riemann-Hilbert problem      N-soliton solutions  
Received:  11 July 2018      Revised:  15 September 2018      Published:  05 December 2018
PACS:  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
  05.45.Yv (Solitons)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 11331008 and 11522112).

Corresponding Authors:  Si-Qi Xu     E-mail:  xsq_zzu@163.com

Cite this article: 

Si-Qi Xu(徐思齐), Xian-Guo Geng(耿献国) N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method 2018 Chin. Phys. B 27 120202

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