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<p>In this paper, an efficient bilinear neural network method (BNNM) is developed for the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation. This method enables the comprehensive derivation of diverse solutions, including breather solutions, lump solutions, and lump-<i>N</i>-soliton solutions (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6167_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\(N\rightarrow \infty\)</EquationSource> </InlineEquation>). By incorporating specific activation functions into a single hidden layer neural network model and employing symbolic computation software, exact solutions can be systematically constructed. Furthermore, the evolutionary behaviors and dynamic characteristics of these solutions are graphically illustrated through suitable parameter selections. The results presented in this study enhance our understanding of the solution structures and provide physical insights into the behavior of the model. These findings also contribute to the exploration of nonlinear wave phenomena in other scientific domains.</p>

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The Excitation of Breather, Lump and Hybrid Solutions for the (2+1)-dimensional BBMB Equation Via Bilinear Neural Network Method

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Long-Xing Li,
  • Bi-Tao Cheng,
  • Guo-Fa Li,
  • Zheng-De Dai

摘要

In this paper, an efficient bilinear neural network method (BNNM) is developed for the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation. This method enables the comprehensive derivation of diverse solutions, including breather solutions, lump solutions, and lump-N-soliton solutions ( \(N\rightarrow \infty\) ). By incorporating specific activation functions into a single hidden layer neural network model and employing symbolic computation software, exact solutions can be systematically constructed. Furthermore, the evolutionary behaviors and dynamic characteristics of these solutions are graphically illustrated through suitable parameter selections. The results presented in this study enhance our understanding of the solution structures and provide physical insights into the behavior of the model. These findings also contribute to the exploration of nonlinear wave phenomena in other scientific domains.