Application of Multivariate Bilinear Neural Network Method to a Spatial Symmetric Nonlinear Dispersive Wave Model in (2 + 1)‐Dimensions

ABSTRACT In this work, the multivariate bilinear neural network method (MBNNM) is applied to derive exact analytical solutions for nonlinear partial differential equations (NPDEs). Specifically, a (2 + 1)‐dimensional spatial symmetric nonlinear dispersive wave model (SSDWM) is investigated by integrating MBNNM with established architectures (3‐2‐2‐1, 3‐2‐3‐1, and 3‐3‐2‐1), while a new 3‐4‐2‐1 architecture is developed for further investigation. By systematically selecting generalized activation functions, diverse exact analytical solutions are obtained, with their dynamic behaviors characterized via 3D/2D plots, contour plots, and density maps. To improve the computational efficiency of MBNNM in handling complex equations, a novel matrix‐based solution strategy is proposed. This strategy significantly enhances computational performance by transforming the Hirota bilinear expansion into matrices for arithmetic processing.