Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise

Hamood Ur Rehman; Aziz Ullah Awan; Sayed M. Eldin; Ifrah Iqbal; Hamood Ur Rehman; Aziz Ullah Awan; Sayed M. Eldin; Ifrah Iqbal

doi:10.3934/math.20231101

AIMS Mathematics

2023, Volume 8, Issue 9: 21606-21621. doi: 10.3934/math.20231101

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Research article

Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise

1.
Department of Mathematics, University of Okara, Okara, Pakistan
2.
Department of Mathematics, University of the Punjab, Lahore, Pakistan
3.
Center of Research, Faculty of Engineering, Future University, New Cairo 11835, Egypt

Received: 22 March 2023 Revised: 05 May 2023 Accepted: 07 May 2023 Published: 07 July 2023
MSC : 35C05, 35C07, 35R11

In many nonlinear partial differential equations, noise or random fluctuation is an inherent part of the system being modeled and have vast applications in different areas of engineering and sciences. This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Itô calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. By using Mathematica 11, some 3D and 2D plots are illustrated to check the influence of multiplicative noise on solutions. The presence of multiplicative noise leads the fluctuations and have significant effects on the long-term behavior of the system. So, it is observed that multiplicative noise stabilizes the solutions of BAE around zero.
- Sardar subequation method (SSM),
- Biswas-Arshed equation (BAE),
- nonlinear evolution equations (NLEEs),
- multiplicative noise
Citation: Hamood Ur Rehman, Aziz Ullah Awan, Sayed M. Eldin, Ifrah Iqbal. Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise[J]. AIMS Mathematics, 2023, 8(9): 21606-21621. doi: 10.3934/math.20231101

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Abstract

In many nonlinear partial differential equations, noise or random fluctuation is an inherent part of the system being modeled and have vast applications in different areas of engineering and sciences. This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Itô calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. By using Mathematica 11, some 3D and 2D plots are illustrated to check the influence of multiplicative noise on solutions. The presence of multiplicative noise leads the fluctuations and have significant effects on the long-term behavior of the system. So, it is observed that multiplicative noise stabilizes the solutions of BAE around zero.

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