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Evolutionary behavior of various wave solutions of the (2+1)-dimensional Sharma–Tasso–Olver equation

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Abstract

In this paper, multiple rogue wave solutions of the (2+1)-dimensional Sharma–Tasso–Olver equation were studied by applying the bilinear neural network method. First, we introduced a single-hidden layer neural network model (NMM) and several types of solutions which can be calculated by this model have been summarized. Additionally, we introduced a “3-2-4” NNM and obtained the solution expression by choosing particular weight coefficients and test functions of the model. Then, through different center of this model, we gave three kinds of rogue wave solutions centered at the origin and three kinds of rogue wave solutions centered with a fixed center. The solutions centered with a fixed center were studied in detail. Finally, several groups of images with physical interpretation, including three-dimensional, contour and density plots exhibited their dynamic structure and physical properties. Furthermore, the obtained results have immensely augmented the exact solutions of the (2+1)-dimensional Sharma–Tasso–Olver equation on the existing literature and enabled us to understand the nonlinear dynamic system deeply, and thus, the proposed method will be a strong boost to the calculation method of nonlinear equations.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (12061054,11661060), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-20-A06) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (2018LH01013).

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Authors and Affiliations

  1. Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, People’s Republic of China

    Y. Y. Feng & S. D. Bilige

  2. School of Software Technology, Dalian University of Technology, Dalian, 116000, People’s Republic of China

    R. F. Zhang

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  1. Y. Y. Feng
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  2. S. D. Bilige
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  3. R. F. Zhang
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Correspondence to S. D. Bilige.

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Feng, Y.Y., Bilige, S.D. & Zhang, R.F. Evolutionary behavior of various wave solutions of the (2+1)-dimensional Sharma–Tasso–Olver equation. Indian J Phys 96, 2107–2114 (2022). https://doi.org/10.1007/s12648-021-02154-6

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  • DOI: https://doi.org/10.1007/s12648-021-02154-6

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