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Breathing wave solutions and Y-type soliton solutions of the \(\varvec{(3+1)}\)-dimensional Ito equation

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Abstract

In this paper, we mainly concentrate on the exact solutions of the \((3+1)\)-dimensional Ito equation for describing certain nonlinear phenomena in fluid dynamics and plasma, including the breathing solutions, the lump solutions, the Y-type soliton solutions, and the interaction solutions between the breathing wave and the Y-type soliton. Particularly, the Y-type soliton solutions and the interaction solutions have been the focus of scholars’ attention recently. Firstly, the single and double breathing wave solutions are given via the three-wave approach. Applying the parametric limit method, the breathing wave solutions are degenerated into lump solutions. Then, the Y-type soliton solutions are constructed based on the N-soliton solutions, which are novel soliton solutions. Next, employing the parametric complex conjugation technique, the N-soliton solutions are transformed into P-breathing wave solutions. Finally, the interaction solutions between breathing waves and Y-type solitons are investigated by the partial degeneration of Y-type soliton solutions. The corresponding visualization graphs exhibit the dynamic behavior of the solutions.

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Acknowledgements

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

Funding

The paper was supported by National Natural Science Foundation of China Nos.  11861013,  11771183,  12261053; Guangxi Science and Technology Base and Talent Project No. AD21238019.

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, China

    Jingyi Cui & Yanfeng Guo

  2. Department of Mathematics, Jiaxing University, Jiaxing, 314001, Zhejiang, China

    Jingjun Zhang

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  1. Jingyi Cui
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  2. Yanfeng Guo
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These authors contributed equally to this work.

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Correspondence to Jingjun Zhang.

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Cui, J., Guo, Y. & Zhang, J. Breathing wave solutions and Y-type soliton solutions of the \(\varvec{(3+1)}\)-dimensional Ito equation. Nonlinear Dyn 111, 22523–22533 (2023). https://doi.org/10.1007/s11071-023-09025-1

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