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General soliton, line breather and (semi-)rational solutions for the nonlocal long-wave-short-wave resonance interaction equation

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Abstract

In this work, the general solutions of the nonlocal long-wave-short-wave resonance interaction (LSRI) equation with nonzero boundary conditions are investigated by using the Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction method. We discussed the cases where N is odd and even, which have a significant impact on the background wave. When N is odd, the solutions are located in the periodic background, while it is on the constant background when N is even. Different forms of solutions are discussed in detail, including the general soliton, line breather and (semi-)rational solutions. For these solutions of the nonlocal LSRI equation, we have obtained a variety of rich and interesting images are obtained through theoretical and graphical analysis, and most of them cannot correspond to the local equation.

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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

The authors would like to thank the editor and referees for their valuable comments and suggestions.

Funding

The work of X. Wu was supported by the China Postdoctoral Science Foundation (No. 2022M710969) and National Science Foundation of China (No.12101159). The work of Y. Chen was supported by the Fundamental Research Funds for the Central Universities (No. 2022FRFK060015).

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  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Xin Wu, Yong Chen & Xue-Wei Yan

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  1. Xin Wu
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Wu, X., Chen, Y. & Yan, XW. General soliton, line breather and (semi-)rational solutions for the nonlocal long-wave-short-wave resonance interaction equation. Nonlinear Dyn 112, 661–679 (2024). https://doi.org/10.1007/s11071-023-09068-4

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