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.