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Dynamics of nonlinear wave and interaction phenomenon in the (\(3 + 1\))-dimensional Hirota–Satsuma–Ito-like equation

  • Regular Article - Nonlinear Dynamics
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Abstract

This paper mainly discussed the (\(3+1\))-dimensional Hirota–Satsuma–Ito-like equation. We obtain the novel lump solution, breather solution and the interaction between the lump solution and solitons and periodic wave. Firstly, the N-soliton solution is obtained based on Bell polynomial and Hirota bilinear. Secondly, on the basis of the multiple soliton solutions, the breather and interaction solution are obtained by using the complex conjugate construction method. We constructed two cases of breather interaction by adjusting appropriate parameters and studied the dynamic behavior of 2 breathers in detail combined with three-dimensional plots and density plots. Finally, by constructing a new positive quadratic function method, we obtained lump solutions and interaction solutions with kink soliton, line soliton, and periodic wave. The interaction between a lump and 1-stripe soliton is especially discussed. These solutions and properties are useful to explain the physical phenomena described by the (\(3+1\))-dimensional HSIl equation. So far, the results obtained in this paper have not been mentioned in previously published research. Our research methods and analytical results enrich the dynamics of the (\(3+1\))-dimensional HSIl equation.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: There are no associated data in this study, and our study is theoretical and analytical investigation of the corresponding theoretical physics model].

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Funding

This study was supported by the Scientific Research Foundation of the Education Department of Sichuan Province, China (Grant No. 15ZB0362).

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Author notes

  1. Binji Wang and Xukun Liu have contributed equally to this work.

Authors and Affiliations

  1. Engineering and Technical College of Chengdu University of Technology, Leshan, 614000, China

    Binji Wang, Zhimin Ma & Xukun Liu

  2. Southwestern Institute of Physics, Chengdu, 610225, China

    Zhimin Ma

Authors
  1. Binji Wang
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  2. Zhimin Ma
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Contributions

BW contributed to conceptualization, methodology, writing—original draft. ZM contributed to formal analysis, supervision, and investigation. XL helped in software.

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Correspondence to Zhimin Ma.

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Wang, B., Ma, Z. & Liu, X. Dynamics of nonlinear wave and interaction phenomenon in the (\(3 + 1\))-dimensional Hirota–Satsuma–Ito-like equation. Eur. Phys. J. D 76, 165 (2022). https://doi.org/10.1140/epjd/s10053-022-00493-5

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