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Riemann–Hilbert approach and N-soliton solutions for a new two-component Sasa–Satsuma equation

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Abstract

A new two-component Sasa–Satsuma equation associated with a \(4\times 4\) matrix spectral problem is proposed by resorting to the zero-curvature equation. Riemann–Hilbert problems are formulated on the basis of spectral analysis of the \(4\times 4\) matrix Lax pair for the two-component Sasa–Satsuma equation, from which zero structures of the Riemann–Hilbert problems are investigated. As applications, N-soliton formulas of the two-component Sasa–Satsuma equation are obtained by solving a particular Riemann–Hilbert problem corresponding to the reflectionless case. Further, the obtained N-soliton formulas are expressed by the ratios of determinants, which are more compact and convenient for symbolic computations. Moreover, the interaction dynamics of the multi-soliton solutions are analyzed and graphically illustrated.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11871440, 11931017).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, 450001, Henan, China

    Jia Wang, Xianguo Geng & Ruomeng Li

  2. College of Science, Henan University of Engineering, 1 Xianghe Road, Zhengzhou, 450001, Henan, China

    Ting Su

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  1. Jia Wang
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Correspondence to Xianguo Geng.

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Wang, J., Su, T., Geng, X. et al. Riemann–Hilbert approach and N-soliton solutions for a new two-component Sasa–Satsuma equation. Nonlinear Dyn 101, 597–609 (2020). https://doi.org/10.1007/s11071-020-05772-7

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  • DOI: https://doi.org/10.1007/s11071-020-05772-7

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