Diversity of exact solutions to the (2+1)-dimensional Ito equation via bilinear neural network method

Abstract

Recently, searching for exact solutions to nonlinear partial differential equations has gradually become a hot research topic. It is of great scientific research and application value to reveal the law of wave propagation, explain natural phenomena accurately and apply related technologies scientifically. In this paper, bilinear neural network method (BNNM) was employed to obtain some new exact analytical solutions to the (2 + 1)-dimensional Ito equation. Based on the Hirota form of Ito equation, we constructed activation functions f in various forms containing the exp(ξ), sin(ξ), cos(ξ), cosh(ξ) and squares of polynomial functions in multi-layer neurons such as [3-2-2] and [3-2-3] neural network models. The test function f in this work is a new expression. On the other hand, these solutions have not been studied yet. As a result, we obtained several new interaction solutions, such as periodic wave solution, breather solution and bright-dark soliton solution, etc. In addition, the corresponding 3D, density and contour plots of all the solution forms were drawn and their characters and dynamic behaviors were vividly demonstrated.