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The N-soliton solutions for the matrix modified Korteweg–de Vries equation via the Riemann–Hilbert approach

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Abstract

This paper focus on seeking the N-soliton solutions for the matrix mKdV equation, which generalizes to the multi-component mKdV equations and the coupled mKdV equations. By utilizing the technique of Riemann–Hilbert and investigating the spectral problem of the Lax pair, a class of Riemann–Hilbert problem will be discussed and established. Finally, in the case of irregularity and reflectionless, we derive the N-soliton solutions for a system of the matrix mKdV equation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11371326 and 11975145).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Xiaotong Chen, Yi Zhang, Jianli Liang & Rui Wang

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  1. Xiaotong Chen
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  2. Yi Zhang
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  3. Jianli Liang
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  4. Rui Wang
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Correspondence to Yi Zhang.

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Chen, X., Zhang, Y., Liang, J. et al. The N-soliton solutions for the matrix modified Korteweg–de Vries equation via the Riemann–Hilbert approach. Eur. Phys. J. Plus 135, 574 (2020). https://doi.org/10.1140/epjp/s13360-020-00575-6

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00575-6

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