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Evolution behaviour of kink breathers and lump-\(\pmb {M}\)-solitons (\(\pmb {M\rightarrow \infty }\)) for the (3+1)-dimensional Hirota–Satsuma–Ito-like equation

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Abstract

In this paper, some novel lump solutions and interaction phenomenon between lump and kink M-soliton are investigated. Firstly, we study the evolution and degeneration behaviour of kink breather wave solution with different forms for the (3+1)-dimensional Hirota–Satsuma–Ito-like equation by symbolic computation and Hirota bilinear form. In the process of degeneration of breather waves, some novel lump solutions are derived by the limit method. In addition, M-fissionable soliton and the interaction phenomenon between lump solutions and kink M-solitons (lump-M-solitons) are investigated, and the theorem and corollary about the conditions for the existence of the interaction phenomenon are given and proved further. The lump-M-solitons with different types are studied to illustrate the correctness and availability of the given theorem and corollary, such as lump-cos type, lump-cosh-exponential type and lump-cosh-cos-cosh type. Several three-dimensional figures are drawn to better depict the nonlinear dynamic behaviours including the oscillation of breather wave, the emergence of lump, the evolution behaviour of fission and fusion of lump-M-solitons and so on.

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The authors declare that data supporting the findings of this study are available within the article, and the figures are concrete expression.

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Acknowledgements

The authors would like to express their sincere thanks to referees for their enthusiastic guidance and help. This work was supported by Scientific and Technological Innovation Team of Nonlinear Analysis and Algebra with Their Applications in Universities of Yunnan Province, China, Grant No. 2020CXTD25.

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  1. College of Mathematics and Statistics, Qujing Normal University, Qujing, 655000, Yunnan, China

    Long-Xing Li

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Li, LX. Evolution behaviour of kink breathers and lump-\(\pmb {M}\)-solitons (\(\pmb {M\rightarrow \infty }\)) for the (3+1)-dimensional Hirota–Satsuma–Ito-like equation. Nonlinear Dyn 107, 3779–3790 (2022). https://doi.org/10.1007/s11071-021-07144-1

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