Qualitative analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative

This study aims to investigate the qualitative behavior analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative. The equation serves as a prominent physics-based mathematical model with numerous practical uses. To analyze the studied equation, we convert it into an ordinary differential equation via traveling wave transformation and then apply the polynomial trial method to deduce its trial equation. Subsequently, the equation with periodically excited perturbation is analyzed using phase trajectory diagrams, bifurcation diagrams, and Lyapunov exponents. Additionally, by utilizing a polynomial complete discrimination system, we derive trigonometric, hyperbolic, and Jacobi elliptic function solutions, some of which are visually represented through figures. These findings enhance the theoretical understanding of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative and contribute to the study of nonlinear wave phenomena.