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<p>This paper explores the Hirota–Satsuma–Ito (HSI) equation, a generalization of well-known equations, presents a comprehensive study of exact solutions using the Hirota Bilinear Operator (HBO) and the Blinear Neural Network Method (BNNM). The derived solutions, have not been found before, include kink solitons, compaction wave solutions, multi-soliton solutions, periodic solitary wave solutions, and hyperbolic solutions. These diverse solutions importantly illustrate the HSI equation’s performance to complex wave phenomena such as localized energy distributions, coherent wave interactions, and periodic oscillations, which are applicable in fields like fluid dynamics, plasma physics, optical systems, and condensed matter physics. The BNNM structure facilitates the systematic derivation of these solutions by transforming the HSI equation into a bilinear form and deploy neural network architectures with activation functions tailored to the behavior of specific solutions. The graphical representations of these solutions show the physical significance, including the localization of energy, symmetry, and periodicity.</p>

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Hirota Bilinear Performance on Hirota–Satsuma–Ito Equation Using Bilinear Neural Network Method

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Nguyen Minh Tuan,
  • Nguyen Hong Son

摘要

This paper explores the Hirota–Satsuma–Ito (HSI) equation, a generalization of well-known equations, presents a comprehensive study of exact solutions using the Hirota Bilinear Operator (HBO) and the Blinear Neural Network Method (BNNM). The derived solutions, have not been found before, include kink solitons, compaction wave solutions, multi-soliton solutions, periodic solitary wave solutions, and hyperbolic solutions. These diverse solutions importantly illustrate the HSI equation’s performance to complex wave phenomena such as localized energy distributions, coherent wave interactions, and periodic oscillations, which are applicable in fields like fluid dynamics, plasma physics, optical systems, and condensed matter physics. The BNNM structure facilitates the systematic derivation of these solutions by transforming the HSI equation into a bilinear form and deploy neural network architectures with activation functions tailored to the behavior of specific solutions. The graphical representations of these solutions show the physical significance, including the localization of energy, symmetry, and periodicity.