Axioms • Vol 14 • No 8
Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method
August 2025 • Mohammed Zakarya, Nadiah Zafer Al-Shehri, Hegagi Mohamed Ali, Mahmoud A. Abd-Rabo, Haytham M. Rezk
This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous balance principle, and the Fe (F-expansion) technique. Leveraging the inherent connection between hypercomplex system (HCS) theory and white noise (WN) analysis, we establish a comprehensive framework for exploring stochastic partial differential equations (PDEs) involving…