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Riemann–Hilbert problems and soliton solutions for the reverse space-time nonlocal Sasa–Satsuma equation

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Abstract

The main work of this paper is to study the soliton solutions and asymptotic behavior of the integrable reverse space-time nonlocal Sasa–Satsuma equation, which is derived from the coupled two-component Sasa–Satsuma system with a specific constraint. The soliton solutions of the nonlocal Sasa–Satsuma equation are constructed through solving the inverse scattering problems by Riemann–Hilbert method. Compared with local systems, discrete eigenvalues and eigenvectors of the reverse space-time nonlocal Sasa–Satsuma equation have novel symmetries and constraints. On the basis of these symmetry relations of eigenvalues and eigenvectors, the one-soliton and two-soliton solutions are obtained and the dynamic properties of these solitons are shown graphically. Furthermore, the asymptotic behaviors of two-soliton solutions are analyzed. All these results about physical features and mathematical properties may be helpful to comprehend nonlocal nonlinear system better.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11905013), the Beijing Natural Science Foundation (No. 1222005), Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University (QXTCP C202118).

Funding

Funding was provided by Beijing Natural Science Foundation (Grant Number 1222005).

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Wen-Xin Zhang, Yaqing Liu, Xin Chen & Shijie Zeng

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  1. Wen-Xin Zhang
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  2. Yaqing Liu
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  3. Xin Chen
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  4. Shijie Zeng
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Correspondence to Yaqing Liu.

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Zhang, WX., Liu, Y., Chen, X. et al. Riemann–Hilbert problems and soliton solutions for the reverse space-time nonlocal Sasa–Satsuma equation. Nonlinear Dyn 111, 10473–10485 (2023). https://doi.org/10.1007/s11071-023-08388-9

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  • DOI: https://doi.org/10.1007/s11071-023-08388-9

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