This paper extends a method, called bilinear neural network method (BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model, specific activation functions of “2-2” model and arbitrary functions of “2-2-3” model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gBKP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots, the evolution characteristic of these waves are exhibited.

本文扩展了一种称为双线性神经网络方法（BNNM）的方法，用于求解非线性偏微分方程的精确解。使用此方法可以构造新的测试功能。这些测试功能由单层模型的特定激活功能，“ 2-2”模型的特定激活功能和“ 2-2-3”模型的任意功能组成。借助BNNM，获得了19组精确的解析解和24维降维的p的任意函数解-gBKP方程是借助Maple通过符号计算获得的。通过选择适当的值可获得分形孤子波，并通过减小观察范围和放大部分图像来观察这些波的自相似特性。通过在单层神经网络模型中提供特定的激活函数，可以获得精确的周期波和呼吸。通过各种三维图，等高线图和密度图，这些波的演化特征得以展现。