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Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation

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Abstract

Under investigation in this paper is a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions. Using the Hirota bilinear method, we construct a bilinear Bäcklund transformation, which consists of four equations and involves six free parameters. With test function method and symbolic computation, three sets of lump–kink solutions and new types of interaction solutions are derived, and figures are presented to reveal the interaction behaviors. Setting constraints to the new interaction solution via the test function expressed by “polynomial-cos-cosh,” we simulate the periodic interaction phenomenon. Pfaffian solutions to the (3+1)-dimensional nonlinear evolution equation are obtained based on a set of linear partial differential conditions. According to our results, the diversity of solutions to the (3+1)-dimensional nonlinear evolution equation is revealed.

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Acknowledgements

This work is supported by the Project of National Training Program of Innovation and Entrepreneurship for Postgraduates (2021YJS172) and the National Natural Science Foundation of China under Grant No. 71971015.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Yu-Hang Yin & Xing Lü

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wen-Xiu Ma

  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Wen-Xiu Ma

  4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Wen-Xiu Ma

  5. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

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  1. Yu-Hang Yin
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Correspondence to Xing Lü or Wen-Xiu Ma.

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Yin, YH., Lü, X. & Ma, WX. Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation. Nonlinear Dyn 108, 4181–4194 (2022). https://doi.org/10.1007/s11071-021-06531-y

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