The main goal of this work was to develop the new analytical neural network technique known as WAS-Exp neural network method. A mathematical analytical technique that could produce solitary, hyperbolic, trigonometric, and rational wave structures in a single framework to build accurate solutions. An essential model for explaining nonlinear wave propagation in dispersive media like optical fibers and plasma channels is the complex hyperbolic nonlinear Schrödinger dynamical equation, which we examined in this work. In contrast to its classical version, the model improves capture memory and non locality and anomalous dispersion by introducing hyperbolic dispersion. We execute the newly proposed technique on this model and a variety of analytical solutions are obtained using this procedure. The resultant solutions provided new insights into the dynamics of nonlinear systems and their possible applications in plasma physics, optical communications, and related domains by demonstrating the wave behavior through the 3D and 2D surfaces. Furthermore, machine learning analysis was executed on the obtained solution for examining the wave dynamic behavior of the actual and predicted outcomes. Lastly, we plotted the x-asymptotic, y-asymptotic and t-asymptotic of the gain solutions through the 2D surfaces.

This paper discusses the generalized non-linear $(3+1)$-dimensional wave equation by modeling and analyzing the dynamics of multi-dimensional nonlinear waves with the WAS-neural network technique. The suggested framework accurately models various wave forms such as bright, singular, and bright-dark solitons. Insofar as we know such neural network based solutions of this model are not reported before. To ensure the reliability and proficiency of the WAS neural network technique. The gain solutions are stable or not by executing the stability analysis on them. The graphical visualization in three-dimensional surface and two-dimensional plots are used. The findings validate that the WAS neural network technique is an efficient and strong alternative to classical techniques of higher-dimensional nonlinear wave equations, and has applications in fluid mechanics and engineering systems that have to deal with gas liquid interactions.