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<p>This work presents an extensive neural network-based analysis of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation, which characterizes the unidirectional shallow water-wave propagation. Bilinear neural network approach is utilized to derive the two types of periodic-soliton solutions and numerous exact solutions obtained from neural network models with single and double hidden layers. Using neural network models, we successfully capture the interaction of lump solutions with double exponent and tangent hyperbola functions, as well as bright and dark solitons and interference wave solutions. For the validity and accuracy of results, we present them in 3D, density, contour and line plots under certain parameter values and constraint conditions. Meanwhile, applied neural network approach effectively derives exact nonlinear wave solutions, contributing to the study of (3+1)-dimensional nonlinear wave fields in mathematical physics and optics.</p>

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Neural network-based explicit solutions to the (3+1)-dimensional Hirota-Satsuma-Ito-like equation

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Muhammad Hamza Rafiq,
  • Ji Lin

摘要

This work presents an extensive neural network-based analysis of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation, which characterizes the unidirectional shallow water-wave propagation. Bilinear neural network approach is utilized to derive the two types of periodic-soliton solutions and numerous exact solutions obtained from neural network models with single and double hidden layers. Using neural network models, we successfully capture the interaction of lump solutions with double exponent and tangent hyperbola functions, as well as bright and dark solitons and interference wave solutions. For the validity and accuracy of results, we present them in 3D, density, contour and line plots under certain parameter values and constraint conditions. Meanwhile, applied neural network approach effectively derives exact nonlinear wave solutions, contributing to the study of (3+1)-dimensional nonlinear wave fields in mathematical physics and optics.