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<p>This paper investigates the (3 + 1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation. It systematically explores the construction of exact solutions and the dynamic characteristics of its complex nonlinear waves. Based on the Hirota bilinear transformation, the original equation is converted into a bilinear form. By integrating the advantages of nonlinear mapping from the bilinear neural network method (BNNM), an efficient solution framework is established, overcoming the limitations of traditional analytical methods that rely on predefined test functions. Through this framework, breather wave solutions, three-wave solutions, and lump-one-kink soliton interaction solutions for the gBKP equation are successfully obtained, systematically revealing the energy reconstruction and transfer regulation mechanisms during wave evolution. This study not only enriches the exact solution family of the gBKP equation and advances the theory of high-dimensional nonlinear localized wave evolution, but also provides methodological and theoretical support for intelligent solving and wave regulation in complex nonlinear systems.</p>

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The Bilinear Neural Network Method for Several Exact Solutions of the (3 + 1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Yanfen Sun,
  • Wei Shi,
  • Xianfen Zhang,
  • Jiaquan Xie

摘要

This paper investigates the (3 + 1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation. It systematically explores the construction of exact solutions and the dynamic characteristics of its complex nonlinear waves. Based on the Hirota bilinear transformation, the original equation is converted into a bilinear form. By integrating the advantages of nonlinear mapping from the bilinear neural network method (BNNM), an efficient solution framework is established, overcoming the limitations of traditional analytical methods that rely on predefined test functions. Through this framework, breather wave solutions, three-wave solutions, and lump-one-kink soliton interaction solutions for the gBKP equation are successfully obtained, systematically revealing the energy reconstruction and transfer regulation mechanisms during wave evolution. This study not only enriches the exact solution family of the gBKP equation and advances the theory of high-dimensional nonlinear localized wave evolution, but also provides methodological and theoretical support for intelligent solving and wave regulation in complex nonlinear systems.