中国物理B ›› 2023, Vol. 32 ›› Issue (4): 40203-040203.doi: 10.1088/1674-1056/ac960a

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Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions

Sha Li(李莎)1, Tiecheng Xia(夏铁成)1,†, and Hanyu Wei(魏含玉)2   

  1. 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
  • 收稿日期:2022-08-05 修回日期:2022-09-27 接受日期:2022-09-29 出版日期:2023-03-10 发布日期:2023-03-17
  • 通讯作者: Tiecheng Xia E-mail:xiatc@shu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11975145), the Program for Science & Technology Innovation Talents in Universities of Henan Province, China (Grant No. 22HASTIT019), the Natural Science Foundation of Henan, China (Grant No. 202300410524), the Science and Technique Project of Henan, China (Grant No. 212102310397), the Academic Degrees & Graduate Education Reform Project of Henan Province, China (Grant No. 2021SJGLX219Y).

Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions

Sha Li(李莎)1, Tiecheng Xia(夏铁成)1,†, and Hanyu Wei(魏含玉)2   

  1. 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
  • Received:2022-08-05 Revised:2022-09-27 Accepted:2022-09-29 Online:2023-03-10 Published:2023-03-17
  • Contact: Tiecheng Xia E-mail:xiatc@shu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11975145), the Program for Science & Technology Innovation Talents in Universities of Henan Province, China (Grant No. 22HASTIT019), the Natural Science Foundation of Henan, China (Grant No. 202300410524), the Science and Technique Project of Henan, China (Grant No. 212102310397), the Academic Degrees & Graduate Education Reform Project of Henan Province, China (Grant No. 2021SJGLX219Y).

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摘要： We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach. The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair. Subsequently, in the case that the Riemann-Hilbert problem is irregular, the N-soliton solutions of the equation can be deduced. In addition, the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.

关键词: complex Sharma-Tasso-Olver equation, Riemann-Hilbert problem, spectral problem, soliton solutions

Abstract: We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach. The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair. Subsequently, in the case that the Riemann-Hilbert problem is irregular, the N-soliton solutions of the equation can be deduced. In addition, the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.

Key words: complex Sharma-Tasso-Olver equation, Riemann-Hilbert problem, spectral problem, soliton solutions

中图分类号:  (Integral equations)

  • 02.30.Rz
02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)