Analyzing the bifurcation, chaos and soliton solutions to (3+1)-dimensional nonlinear hyperbolic Schrödinger equation

Water wave development, soliton dynamics and electromagnetic field propagation are just a few phenomena that are studied using the (3+1)-dimensional nonlinear hyperbolic Schrödinger model (NLHSM). This work extracts unique soliton solutions such as solitary, dark periodic, combination of dark and bright solutions, and rational wave solutions by analyzing the NLHSM using the modified Sardar sub-equation technique (MSSET). Also, the chaotic structure for the governing model is examined with and without disturbance using chaos theory and bifurcation theory. The innovations of our research are in discovering hitherto unexplored bifurcation situations and chaotic behaviors within the governing equation. The focus of these investigations is on the solutions of nonlinear dynamics, which are illustrated using density plots, 3-D plots, 2-D curves, and pertinent physical property descriptions. Outcomes demonstrate the value of NLHSM for generating soliton solutions and evaluating them in nonlinear models, offering useful numerical tools for applied mathematics.