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<p>Finding exact analytic solutions of nonlinear differential equations, one of the fields that are significantly important to mechanic engineering and dynamic systems, has been a focus in the past eras. The Benney-Luke equation representing the propagation of water wave surface is solved by many methods yielding diverse solutions. This paper presents a new extended form of the Benney-Luke equation and the exact analytic solutions are obtained using the bilinear neural network technique regarding the definition of Hirota bilinear form. The various solutions are established and produced by constructing activation functions consistent with the processing procedure. The solutions are depicted and compared in two and three dimensions to investigate the behaviors.</p>

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Bilinear Recurrent Neural Network for a Modified Benney-Luke Equation

  • 期刊论文

  • 发表日期：

    2025年2月22日

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  • Nguyen Minh Tuan,
  • Phayung Meesad

摘要

Finding exact analytic solutions of nonlinear differential equations, one of the fields that are significantly important to mechanic engineering and dynamic systems, has been a focus in the past eras. The Benney-Luke equation representing the propagation of water wave surface is solved by many methods yielding diverse solutions. This paper presents a new extended form of the Benney-Luke equation and the exact analytic solutions are obtained using the bilinear neural network technique regarding the definition of Hirota bilinear form. The various solutions are established and produced by constructing activation functions consistent with the processing procedure. The solutions are depicted and compared in two and three dimensions to investigate the behaviors.