Bifurcation, chaotic analysis and soliton solutions to the (3+1)-dimensional p-type model

This study examines the modified Sardar sub-equation method (MSSEM) for deriving the novel solutions of the (3+1)-dimensional p-type model. This framework is commonly employed to explain the behavior of optical solitons in nonlinear media. The applications of MSSEM allows us to acquire the precise analytical solutions, which incorporate a diverse array of optical soliton solutions. We discuss the dynamical structure of the solitons, bifurcation and chaos theory to develop the multiple soliton solutions, including rational, hyperbolic, exponential, and trigonometric functions and depending on the principle of balancing equation. Moreover, by using bifurcation and chaos theory, we examine the governing model with and without the perturbation term and provide the three-dimensional, two-dimensional, and density profiles to improve the clarity of obtained results. The different aspects of the solutions are evident in our visual representations. These solutions are applicable to a wide range of domains, including fluid physics, oceanography, physics, engineering, and nonlinear optics.