A Bilinear Neural Network Method for Solving a Generalized Fractional (2+1)-Dimensional Konopelchenko-Dubrovsky-Kaup-Kupershmidt Equation

Abstract

The bilinear neural network method (BNNM), an approach of machine learning technique, includes the construction of an extended homoclinic test approach (EHTA) to attain the solutions of a generalized fractional (2+1)-dimensional Konopelchenko - Dubrovsky - Kaup - Kupershmidt (gfKDKK) equation which plays a pivotal role in the study of dynamics and plasma physics. The technique provides a new construction focused on finding solutions to the gfKDKK equation using the BNNM. Based on an EHTA formulation, BNNM offers an open, straightforward, and varied approach to building test functions and collecting solutions. In this study, the solutions obtained are constructed on the expression of Hirota’s bilinear operator, which encompasses a variety of solutions such as peak soliton solution, solitary wave solution, and periodic soliton solutions. The BNNM’s ability to generate diverse solutions highlights its versatility and potential for addressing complex nonlinear partial differential equations. The visualization is graphed in 3D and 1D contour using a Python application to investigate the behavior of the solutions.