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High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method

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Abstract

The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this article, we mainly investigate the third-order flow GI equation. In the framework of the Riemann-Hilbert method, the soliton matrices of the third-order flow GI equation with simple zeros and elementary high-order zeros of Riemann-Hilbert problem are constructed through the standard dressing process. Taking advantage of this result, some properties and asymptotic analysis of single soliton solution and two soliton solution are discussed, and the simple elastic interaction of two soliton are proved. Compared with soliton solution of the classical second-order flow, we find that the higher-order dispersion term affects the propagation velocity, propagation direction and amplitude of the soliton. Finally, by means of a certain limit technique, the high-order soliton solution matrix for the third-order flow GI equation is derived.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200062, China

    **-yan Zhu & Yong Chen

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yong Chen

Authors
  1. **-yan Zhu
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  2. Yong Chen
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Correspondence to Yong Chen.

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The authors declare no conflict of interest.

Additional information

The project is supported by the National Natural Science Foundation of China (No. 12175069 and No. 12235007) and Science and Technology Commission of Shanghai Municipality (No. 21JC1402500 and No. 22DZ2229014), and Natural Science Foundation of Shanghai, China (No. 23ZR1418100).

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Zhu, Jy., Chen, Y. High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method. Acta Math. Appl. Sin. Engl. Ser. 40, 358–378 (2024). https://doi.org/10.1007/s10255-024-1109-4

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  • DOI: https://doi.org/10.1007/s10255-024-1109-4

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