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The mixed solutions of the (2+1)-dimensional Hirota–Satsuma–Ito equation and the analysis of nonlinear transformed waves

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Abstract

In this paper, we obtain the N-soliton solution for the \((2+1)\)-dimensional Hirota–Satsuma–Ito equation by the Hirota bilinear method. On this basis, the breathers and lumps can be obtained using the complex conjugate parameter as well as the long wave limit method, and the mixed solutions containing them are investigated. Then, different nonlinear transformed waves are obtained from breathers and lumps under specific conditions, which include quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, quasi-periodic soliton and W-shaped soliton. Finally, on the basis of the two-breather solutions, we discuss in detail the mixed solutions consisting of one breather and one nonlinear transformed wave, and the mixed solutions formed by two nonlinear transformed waves.

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Acknowledgements

We express our sincere thanks to each member of our discussion group for their suggestions. This work has been supported by the National Natural Science Foundation of China under Grant No. 11905155, and the Fund Program for the Scientific Activities of Selected Returned Overseas Scholars in Shanxi Province under Grant No. 20220008.

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This work has been supported by the National Natural Science Foundation of China under Grant No. 11905155, the Fund Program for the Scientific Activities of Selected Returned Overseas Scholars in Shanxi Province under Grant No. 20220008.

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  1. School of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Yong-Ning An & Rui Guo

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An, YN., Guo, R. The mixed solutions of the (2+1)-dimensional Hirota–Satsuma–Ito equation and the analysis of nonlinear transformed waves. Nonlinear Dyn 111, 18291–18311 (2023). https://doi.org/10.1007/s11071-023-08791-2

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