Analyzing multiplicative noise effects on stochastic dynamical ϕ4 equation using the new extended direct algebraic method

Zuha Manzoor; Muhammad Sajid Iqbal; Nader Omer; Mohammed Zakarya; Mohammad Kanan; Ali Akgül; Shabbir Hussain; Farrah Ashraf

Alexandria Engineering Journal (Jun 2024)

Analyzing multiplicative noise effects on stochastic dynamical ϕ4 equation using the new extended direct algebraic method

Zuha Manzoor,
Muhammad Sajid Iqbal,
Nader Omer,
Mohammed Zakarya,
Mohammad Kanan,
Ali Akgül,
Shabbir Hussain,
Farrah Ashraf

Affiliations

Zuha Manzoor: Department of Mathematics and Statistics, University of Lahore, Pakistan
Muhammad Sajid Iqbal: School of Foundation Studies and Mathematics, OUC with Liverpool John Moores University (UK) Qatar Campus, 12253 Doha, Qatar; Department of H & BS, Military College of Signals, NUST, Islamabad, Pakistan
Nader Omer: Department of Information Systems, College of Computing and Information Technology, University of Bisha, Bisha 61922, Saudi Arabia
Mohammed Zakarya: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Corresponding author.
Mohammad Kanan: Department of Industrial Engineering, College of Engineering, University of Business and Technology, Jeddah 21448, Saudi Arabia; Department of Mechanical Engineering, College of Engineering, Zarqa University, Zarqa, Jordan
Ali Akgül: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
Shabbir Hussain: Department of Mathematics and Statistics, University of Lahore, Pakistan
Farrah Ashraf: Department of Mathematics and Statistics, University of Lahore, Pakistan

Journal volume & issue: Vol. 97
pp. 185 – 203

Abstract

Read online

The stochastic dynamical ϕ4 equation is obtained by adding a multiplicative noise term to the classical ϕ4 equation. The noise term represents the random fluctuations that are present in the system and is modeled by a Wiener process. The stochastic dynamical ϕ4 equation is a powerful tool for modeling the behavior of complex systems that exhibit randomness and nonlinearity. It has a wide range of applications in physics, chemistry, biology, and finance. Our goal of this paper is to use the new extended direct algebraic method to find the stochastic traveling wave solutions of the dynamical ϕ4 equation. We explore the new trigonometric, hyperbolic, and rational functions using the new extended direct algebraic method. Furthermore, we use Matlab to plot 3D surfaces of exact solutions to show how multiplicative noise affects the solutions to the stochastic dynamical ϕ4 equation.

Published in Alexandria Engineering Journal

ISSN: 1110-0168 (Print); 2090-2670 (Online)
Publisher: Elsevier
Country of publisher: Egypt
LCC subjects: Technology: Engineering (General). Civil engineering (General)
Website: http://www.journals.elsevier.com/alexandria-engineering-journal/

About the journal

Abstract

Keywords