This paper presents a bilinear neural network architecture (BNNA) to analyze the (2+1) -dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. The suggested framework integrates the Hirota bilinear formulation (HBF) and a neural network (NN) representation in which the bilinear structure is maintained and the neural weights are adjustable symbolic coefficients. One hidden-layer architecture is used, namely, 3\!-\!3\!-\!1. With this method, a number of closed-form wave solutions are found, such as lump, lump-kink, interaction, three-soliton, and breather-like interaction structures. The outcomes are able to capture important nonlinear characteristics like localization, interaction dynamics, and periodic behavior. These solutions have dynamical properties that are depicted using three-dimensional (3D) surface and contour plots. In general, the suggested BNNA offers a straightforward, understandable, and effective model for building analytical solutions of nonlinear partial differential equations (NLPDEs) through the combination of HBF and NN-based representation.
Ali et al. (Thu,) studied this question.