Non-Gaussian White Noise Functional Solutions of χ -Wick-Type Stochastic KdV Equations

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