Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation

Abstract

The bilinear neural network method is a novel approach for obtaining exact analytical solutions to nonlinear evolution equations. This method leverages neural networks to transform nonlinear partial differential equations (PDEs) into bilinear forms, which can then be solved analytically.  The key advantage of this method is its ability to handle complex nonlinearities efficiently, providing a systematic way to derive exact solutions that were previously difficult to obtain