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.
Highlights
IntroductionIn order to obtain the exact solutions of random (3+1)-dimensional modified BBM equations, we only consider them in a white noise environment; that is, we will discuss the Wick-type, stochastic,
By an application example, we show how the stochastic solutions can be given as white noise functional solutions
We set up a new and general version of the modified tanh–coth method to deal with the nonlinear multi dimensional partial differential equations (PDEs)
Summary
In order to obtain the exact solutions of random (3+1)-dimensional modified BBM equations, we only consider them in a white noise environment; that is, we will discuss the Wick-type, stochastic,. El-Wakil [36] and Soliman [37] modified the tanh–coth method and presented new, exact solutions for some nonlinear PDEs. Our aim in this work was to obtain new stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations.
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