Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations

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...

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Bibliographic Details
Published in:Axioms 2019-12, Vol.8 (4), p.134
Main Authors: Agarwal, Praveen, Hyder, Abd-Allah, Zakarya, M., AlNemer, Ghada, Cesarano, Clemente, Assante, Dario
Format: Article
Language:English
Subjects:
Acoustics
Exact solutions
Fluid mechanics
Gravity waves
Mathematical analysis
Mathematical functions
Noise
Partial differential equations
Traveling waves
White noise
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms8040134