Abundant novel stochastic fractional solitary wave solutions of a new extended (3+1)-dimensional Kadomtsev–Petviashvili equation - Amjad E. Hamza; Khidir Shaib Mohamed; Alaa Mustafa; Khaled Aldwoah; Mohammed Hassan; Hicham Saber (Alexandria Engineering Journal)
The (3+1)-dimensional Kadomtsev–Petviashvili equation arises in various physical contexts, including fluid mechanics, plasma physics, and nonlinear optics. Exact solutions play a vital role in understanding the physical behavior of a system. The conformable derivative generalizes the classical differential operator and is useful in analyzing the wave dynamics of integrable systems. In this article, the modified extended tanh technique is implemented to uncover new solitary wave solutions of the KP equation. The results obtained via modified extended tanh technique yield bright, dark, and periodic solitary waves. Additionally, we implement the generalized Kudryashov technique to deduce more solitary wave solutions of the considered equation. The solutions obtained using the generalized Kudryashov method exhibit horse-shoe-like, bell-shaped, and W-shaped solitary waves. The obtained results are simulated both with and without the effect of noise, and are displayed in 3D and 2D graphs. The effect of the conformable fractional order on the amplitude and propagation of the solitary waves is visualized via these graphs.