Interaction phenomenon for variable coefficient Kadomtsev-Petviashvili equation by utilizing variable coefficient bilinear neural network method

TL;DR

This paper introduces a variable coefficient bilinear neural network approach to find analytical solutions for variable coefficient nonlinear PDEs, demonstrated on the Kadomtsev-Petviashvili equation, revealing complex dynamics through graphical analysis.

Contribution

It develops a novel neural network method for solving variable coefficient nonlinear PDEs and applies it to derive analytical solutions for the KP equation with variable coefficients.

Findings

Rich analytical solutions obtained for the variable coefficient KP equation

Demonstrated complex dynamics through graphical visualization

Established models with specific parameter choices to explore solution behaviors

Abstract

In this paper, a variable coefficient Bilinear neural network method is proposed to deal with the analytical solutions of variable coefficient nonlinear partial differential equations. As an example, a Kadomstev-Petviashvili equation with variable coefficients is investigated by using the variable coefficient Bilinear neural network method. By establishing "3-2-2-1" and "3-3-2-1" models respectively, rich analytical solutions of the variable coefficient Kadomstev-Petviashvili equation are obtained. By choosing some special values of the parameters, the dynamics properties are demonstrated in some three-dimensional and density graphics.