Exact solutions for a class ofwick-type stochastic (3+1)-dimensional modified benjamin-bona-mahony equations

Abstract

In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin-Bona-Mahony (BBM) equations. We present a generalised version of the modified tanh-coth method. Using the generalised, modified tanh-coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions.