SOLITON SOLUTIONS FOR THE HIGHER DIMENSIONAL FRACTIONAL CONFORMABLE STOCHASTIC MODIFIED KORTEWEG–DE VRIES–ZAKHAROV–KUZNETSOV MODEL

The stochastic conformable fractional modified Korteweg–de Vries Zakharov–Kuznetsov (KdV–ZK) equation, which accurately simulates nonlinear, multidimensional wave propagation impacted by randomness, is the main topic of this investigation. The KdV–ZK equation is an effective model for modulating nonlinear waves in a wide range of physical systems, including plasma physics, atmospheric science, fluid dynamics, soliton theory, and optical fibers. The proposed techniques can extract multiple novel solutions to the KdV–ZK equation, which is critical for gaining fresh insights into physical problems. Furthermore, the recommended extension shortens the calculation time and improves computational efficiency. The produced solitons have potential uses in a variety of scientific and technological domains. By integrating conformable calculus with stochastic analysis, we investigate both exact and approximate solutions by numerical simulations and stability evaluations. The model enhances classical wave equations by incorporating conformable derivatives and multiplicative noise, analyzed in the Stratonovich sense. We derive new stochastic solutions expressed through elliptic, hyperbolic, trigonometric, and rational functions. These solutions reveal a variety of complex wave structures, including periodic, dark, v-shaped, optical, dazzling, and isolated solitons. The findings confirm that the proposed approaches are efficient and dependable for addressing intricate nonlinear stochastic fractional models.