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

Abstract

In this work, a more accurate analytical solution of nonlinear par-tial differential equation is sought by setting the generalized activation func-tion 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 so-lutions with arbitrary activation functions are obtained by selecting differentactivation functions and the dynamical properties are demonstrated throughthree-dimensional, two-dimensional and density plots. 2010 Mathematics Subject Classification: 35Q51, 35G99, 33F10