Next Article in Journal
A Fast Multilevel Fuzzy Transform Image Compression Method
Previous Article in Journal
Synthetic Tableaux with Unrestricted Cut for First-Order Theories
Previous Article in Special Issue
Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces
Open AccessArticle

Exact Solutions for a Class of Wick-Type Stochastic (31)-Dimensional Modified Benjamin–Bona–Mahony Equations+

1
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
2
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
3
Department of Engineering Mathematics and Physics, Faculty of Engineering Al-Azhar University, Cairo P.O. Box 11371, Egypt
4
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut P.O. Box 71524, Egypt
5
Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia
6
Section of Mathematics, Università Telematica Internazionale Uninettuno, 00186 Rome, Italy
7
Faculty of Engineering, Università Telematica Internazionale Uninettuno, 00186 Rome, Italy
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(4), 134; https://doi.org/10.3390/axioms8040134
Received: 9 October 2019 / Revised: 9 November 2019 / Accepted: 18 November 2019 / Published: 3 December 2019
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
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. View Full-Text
Keywords: modified BBM equations; (3+1)-dimensional equations; white noise; Brownian motion; travelling wave solutions; wick-type stochastic modified BBM equations; (3+1)-dimensional equations; white noise; Brownian motion; travelling wave solutions; wick-type stochastic
MDPI and ACS Style

Agarwal, P.; Hyder, A.-A.; Zakarya, M.; AlNemer, G.; Cesarano, C.; Assante, D. Exact Solutions for a Class of Wick-Type Stochastic (31)-Dimensional Modified Benjamin–Bona–Mahony Equations+. Axioms 2019, 8, 134.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop