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<p>This paper presents a bilinear neural network architecture (BNNA) to analyze the <InlineEquation ID="IEq1"><EquationSource Format="TEX">\((2+1)\)</EquationSource></InlineEquation>-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. The suggested framework integrates the Hirota bilinear formulation (HBF) and a neural network (NN) representation in which the bilinear structure is maintained and the neural weights are adjustable symbolic coefficients. One hidden-layer architecture is used, namely, <InlineEquation ID="IEq2"><EquationSource Format="TEX">\([3\!-\!3\!-\!1]\)</EquationSource></InlineEquation>. With this method, a number of closed-form wave solutions are found, such as lump, lump-kink, interaction, three-soliton, and breather-like interaction structures. The outcomes are able to capture important nonlinear characteristics like localization, interaction dynamics, and periodic behavior. These solutions have dynamical properties that are depicted using three-dimensional (3D) surface and contour plots. In general, the suggested BNNA offers a straightforward, understandable, and effective model for building analytical solutions of nonlinear partial differential equations (NLPDEs) through the combination of HBF and NN-based representation.</p>

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Physics-Guided Bilinear Neural Network for Soliton and Breather Dynamics in the (2+1)-Dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月7日

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  • Asad Ali,
  • Ibtehal Alazman,
  • Numan Ahmed,
  • Syed T. R. Rizvi,
  • Ibtisam Aldawish,
  • Aly R. Seadawy

摘要

This paper presents a bilinear neural network architecture (BNNA) to analyze the \((2+1)\)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. The suggested framework integrates the Hirota bilinear formulation (HBF) and a neural network (NN) representation in which the bilinear structure is maintained and the neural weights are adjustable symbolic coefficients. One hidden-layer architecture is used, namely, \([3\!-\!3\!-\!1]\). With this method, a number of closed-form wave solutions are found, such as lump, lump-kink, interaction, three-soliton, and breather-like interaction structures. The outcomes are able to capture important nonlinear characteristics like localization, interaction dynamics, and periodic behavior. These solutions have dynamical properties that are depicted using three-dimensional (3D) surface and contour plots. In general, the suggested BNNA offers a straightforward, understandable, and effective model for building analytical solutions of nonlinear partial differential equations (NLPDEs) through the combination of HBF and NN-based representation.