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

Authors

Hossam A. Ghany, Department of Mathematics, Helwan University, Cairo, EgyptFollow
Abd-Allah Hyder, Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt.Follow
M. Zakarya, Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.Follow

Author Country (or Countries)

Egypt.

Abstract

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)

http://dx.doi.org/10.18576/amis/110332

Recommended Citation

A. Ghany, Hossam; Hyder, Abd-Allah; and Zakarya, M. (2017) "Non-Gaussian White Noise Functional Solutions of χ -Wick-Type Stochastic KdV Equations," Applied Mathematics & Information Sciences: Vol. 11: Iss. 3, Article 32.
DOI: http://dx.doi.org/10.18576/amis/110332
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss3/32