Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations. (February 2020)

• Record Type: Journal Article
• Authors: Kim, Hyunsoo; Sakthivel, Rathinasamy; Debbouche, Amar; Torres, Delfim F.M.
• Is Part Of: Chaos, solitons and fractals. Volume 131(2020)
• Publication Date: 2020-02
• Subjects: Wick-type stochastic nonlinear Schrödinger equation -- Wick-type stochastic fractional RLW-Burgers equation -- Travelling wave solutions -- Hermite transform -- Solitary waves; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.109542
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schrödinger equation and of a Wick-type stochastic fractional Regularized Long Wave-Burgers (RLW-Burgers) equation have been obtained by using an improved computational method. Specifically, the Hermite transform is employed for transforming Wick-type stochastic nonlinear partial differential equations into deterministic nonlinear partial differential equations with integral and fraction order. Furthermore, the required set of stochastic solutions in the white noise space is obtained by using the inverse Hermite transform. Based on the derived solutions, the dynamics of the considered equations are performed with some particular values of the physical parameters. The results reveal that the proposed improved computational technique can be applied to solve various kinds of Wick-type stochastic fractional partial differential equations.