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Simple and high-order N-solitons of the nonlocal generalized Sasa–Satsuma equation via an improved Riemann–Hilbert method

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Abstract

In this paper, we investigate the nonlocal generalized Sasa–Satsuma (ngSS) equation based on an improved Riemann–Hilbert method (RHM). Different from the traditional RHM, the t-part of the Lax pair plays a more important role rather than the x-part in analyzing the spectral problems. So we start from the t-part of the spectral problems. In the process of dealing with the symmetry reductions, we are surprised to find that the computation is much less than the traditional RHM. We can more easily derive the compact expression of N-soliton solution of the ngSS equation under the reflectionless condition. In addition, the general high-order N-soliton solution of the ngSS equation is also deduced by means of the perturbed terms and limiting techniques. We not only demonstrate different cases for the dynamics of these solutions in detail in theory, but also exhibit the remarkable features of solitons and breathers graphically by demonstrating their 3D, projection profiles and wave propagations. Our results should be significant to understand the nonlocal nonlinear phenomena and provide a foundation for fostering more innovative research that advances the theory.

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The authors declare that all data supporting the findings of this study are available within the article.

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Acknowledgements

This work of the first author was supported by the National Natural Science Foundation of China (No.12271129) and the China Scholarship Council (No.202206120152). The work of the second author was supported by the National Natural Science Foundation of China (No.12201622). The work of the third author was supported by the China Postdoctoral Science Foundation (2023M733404), the Young Innovative Talents Project of Guangdong Province of China (2022KQNCX104) and the Guangdong Basic and Applied Basic Research Foundation (2022A1515111209). The work of the fourth author was supported by the National Natural Science Foundation of China (No.12271129). The first author appreciates the hospitality of the Department of Mathematics, National University of Singapore, where the work was done.

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Authors and Affiliations

  1. School of Science, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Guixian Wang

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Guixian Wang & Bo Han

  3. Department of Mahematics, National University of Singapore, Singapore, 119076, Singapore

    Guixian Wang

  4. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    Xiu-Bin Wang

  5. Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, 518172, Shenzhen, China

    Haie Long

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  1. Guixian Wang
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Correspondence to Bo Han.

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This work is supported by the National Natural Science Foundation of China (No.12271129 and No.12201622), the China Scholarship Council (No.202206120152), the China Postdoctoral Science Foundation (No.2023M733404), the Young Innovative Talents Project of Guangdong Province of China (No.2022KQNCX104) and the Guangdong Basic and Applied Basic Research Foundation (No.2022A1515111209).

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Wang, G., Wang, XB., Long, H. et al. Simple and high-order N-solitons of the nonlocal generalized Sasa–Satsuma equation via an improved Riemann–Hilbert method. Z. Angew. Math. Phys. 75, 94 (2024). https://doi.org/10.1007/s00033-024-02235-6

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