Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

TL;DR

This paper derives exact traveling wave solutions for Wick-type stochastic nonlinear PDEs using an improved computational method involving Hermite transforms, demonstrating the method's effectiveness for stochastic fractional equations.

Contribution

It introduces an improved computational approach employing Hermite transforms to solve Wick-type stochastic fractional PDEs, providing explicit solutions and analyzing their dynamics.

Findings

Exact solutions for stochastic nonlinear Schrödinger and RLW-Burgers equations.

The proposed method effectively solves Wick-type stochastic fractional PDEs.

Solutions reveal the influence of physical parameters on equation dynamics.

Abstract

In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schr\"{o}dinger 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.