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Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation

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Abstract

It is well known that most classical test functions to solve nonlinear partial differential equations can be constructed via single hidden layer neural network model by using Bilinear Neural Network Method (BNNM). In this paper, the neural network model of test function for the (3+1)-dimensional Jimbo–Miwa equation is extended to the “4-2-3” model. By giving some specific activation functions, new test function is constructed to obtain analytical solutions of the (3+1)-dimensional Jimbo–Miwa equation. Rogue wave solutions and the bright and dark solitons are obtained by giving some specific parameters. Via curve plots, three-dimensional plots, contour plots and density plots, dynamical characteristics of these waves are exhibited.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos.: 61572095 and 61877007.

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Authors and Affiliations

  1. School of Software Technology, Dalian University of Technology, Dalian, 116620, China

    Run-Fa Zhang & Ming-Chu Li

  2. Department of Mechanical Engineering, University of Hong Kong, Pok Fu Lam, Hong Kong, China

    Hui-Min Yin

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  1. Run-Fa Zhang
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Zhang, RF., Li, MC. & Yin, HM. Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation. Nonlinear Dyn 103, 1071–1079 (2021). https://doi.org/10.1007/s11071-020-06112-5

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  • DOI: https://doi.org/10.1007/s11071-020-06112-5

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