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<p>In this article, the constant coefficient (2+1)-dimensional Graphene sheets equation is considered to explore its novel soliton solutions using an advanced computation technique known as the bilinear neural network method. The bilinear form of the proposed model is established, and a variety of soliton solutions are extracted by employing different neural network structures. The single hidden layer neural network structures “3-3-1” and “3-4-1” with different test functions are considered to explore solutions to breather wave, M-lump, and lump interaction solutions. For more complex investigation, the double hidden layer neural network structure “3-2-3-1” with different test functions is considered to explore rogue wave and breather wave solutions. This nonlinear evaluation model has many applications in nanotechnology. This investigation provides new insights into the dynamics of graphene sheets. The bilinear neural network method offers clear insight into the dynamics of complex nonlinear physical systems. The findings of this research are helpful for understanding the nonlinear phenomena in materials science, applied mathematics, and nanotechnology. Moreover, the observable physical behaviour of certain solutions is illustrated through 3D, 2D, density, and contour plots.</p>

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Exploring breather, M-lump, lump interaction, and rogue wave phenomena for the constant coefficients (2+1)-dimensional Graphene sheets equation via neural networking

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Muhammad Qasim,
  • Fengping Yao,
  • Muhammad Zafarullah Baber

摘要

In this article, the constant coefficient (2+1)-dimensional Graphene sheets equation is considered to explore its novel soliton solutions using an advanced computation technique known as the bilinear neural network method. The bilinear form of the proposed model is established, and a variety of soliton solutions are extracted by employing different neural network structures. The single hidden layer neural network structures “3-3-1” and “3-4-1” with different test functions are considered to explore solutions to breather wave, M-lump, and lump interaction solutions. For more complex investigation, the double hidden layer neural network structure “3-2-3-1” with different test functions is considered to explore rogue wave and breather wave solutions. This nonlinear evaluation model has many applications in nanotechnology. This investigation provides new insights into the dynamics of graphene sheets. The bilinear neural network method offers clear insight into the dynamics of complex nonlinear physical systems. The findings of this research are helpful for understanding the nonlinear phenomena in materials science, applied mathematics, and nanotechnology. Moreover, the observable physical behaviour of certain solutions is illustrated through 3D, 2D, density, and contour plots.