A fourth-order nonlinear equation studied by using a multivariate bilinear neural network method

In this work, a more accurate analytical solution of nonlinear partial differential equation is sought by setting the generalized activation function in the model of multiple bilinear neural network method. As an example, the 3-2-2-1, 3-2-3-1, 3-3-2-1 and 3-3-3-1 models are selected to study the new (2+1) dimensional nonlinear wave equation equations. Exact analytical solutions with arbitrary activation functions are obtained by selecting different activation functions and the dynamical properties are demonstrated through three-dimensional, two-dimensional and density plots.