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N-Soliton Solution of The Kundu-Type Equation Via Riemann-Hilbert Approach

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Abstract

In this article, we focus on investigating the Kundu-type equation with zero boundary condition at infinity. Based on the analytical and symmetric properties of eigenfunctions and spectral matrix of its Lax pair, a Riemann-Hilbert problem for the initial value problem of the Kundu-type equation is constructed. Further through solving the regular and nonregular Riemann-Hilbert problem, a kind of general N-soliton solution of the Kundu-type equation are presented. As special cases of this result, the N-soliton solution of the Kaup-Newell equation, Chen-Lee-Liu equation, and Gerjikov-Ivanov equation can be obtained respectively by choosing different parameters.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Lili Wen & Engui Fan

  2. Department of Basic Courses, Shandong University of Science and Technology, Taian, 266510, China

    Ning Zhang

Authors
  1. Lili Wen
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  2. Ning Zhang
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  3. Engui Fan
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Corresponding author

Correspondence to Engui Fan.

Additional information

This work was supported by the National Science Foundation of China (11671095, 51879045, 11805114).

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Wen, L., Zhang, N. & Fan, E. N-Soliton Solution of The Kundu-Type Equation Via Riemann-Hilbert Approach. Acta Math Sci 40, 113–126 (2020). https://doi.org/10.1007/s10473-020-0108-x

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  • DOI: https://doi.org/10.1007/s10473-020-0108-x

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