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Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method

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Abstract

This paper extends a method, called bilinear neural network method (BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model, specific activation functions of “2-2” model and arbitrary functions of “2-2-3” model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gBKP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots, the evolution characteristic of these waves are exhibited.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, China

    Runfa Zhang & Sudao Bilige

  2. College of Art and Sciences, Shanghai Maritime University, Shanghai, 201306, China

    Temuer Chaolu

Authors
  1. Runfa Zhang
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  2. Sudao Bilige
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  3. Temuer Chaolu
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Corresponding author

Correspondence to Sudao Bilige.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11661060, 11571008, the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No. NJYT-20-A06 and the Natural Science Foundation of Inner Mongolia Autonomous Region of China under Grant No. 2018LH01013.

This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.

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Zhang, R., Bilige, S. & Chaolu, T. Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method. J Syst Sci Complex 34, 122–139 (2021). https://doi.org/10.1007/s11424-020-9392-5

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  • DOI: https://doi.org/10.1007/s11424-020-9392-5

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