In this paper, KdV equations with variable coefﬁcients and Wick-type stochastic KdV equations are investigated. White noise functional solutions are shown by Hermite transform, homogeneous balance principle and F-expansion method. By means of the direct connection between the theory of hypercomplex systems and white noise analysis, we setup a full framework to study the stochastic partial differential equations with non-Gaussian parameters. Using this framework and F-expansion method, we present multiple families of exact and stochastic travelling wave solutions for the variable coefﬁcients KdV equations and the stochastic KdV equations with non-Gaussian parameters, respectively. These solutions include functional solutions of Jacobi elliptic functions (JEFs), trigonometric and hyperbolic types.
Digital Object Identifier (DOI)
A. Ghany, Hossam; Hyder, Abd-Allah; and Zakarya, M.
"Non-Gaussian White Noise Functional Solutions of χ -Wick-Type Stochastic KdV Equations,"
Applied Mathematics & Information Sciences: Vol. 11
, Article 67.
Available at: https://dc.naturalspublishing.com/amis/vol11/iss3/67