New and effective solitary applications in Schrödinger equation via Brownian motion process with physical coefficients of fiber optics

Yousef F. Alharbi; E. K. El-Shewy; Mahmoud A. E. Abdelrahman; Yousef F. Alharbi; E. K. El-Shewy; Mahmoud A. E. Abdelrahman

doi:10.3934/math.2023205

AIMS Mathematics

2023, Volume 8, Issue 2: 4126-4140. doi: 10.3934/math.2023205

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Research article

New and effective solitary applications in Schrödinger equation via Brownian motion process with physical coefficients of fiber optics

1.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2.
Department of Physics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
3.
Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura, Egypt
4.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 25 September 2022 Revised: 07 November 2022 Accepted: 15 November 2022 Published: 01 December 2022
MSC : 78A10, 35C07, 60H15, 60H30, 60H40, 35Q55, 35Q60

Using the unified solver technique, the rigorous and effective new novel optical progressive and stationary structures are established in the aspects of hyperbolic, trigonometric, rational, periodical and explosive types. These types are concrete in the stochastic nonlinear Schrödinger equations (NLSEs) with operative physical parameters. The obtained stochastic solutions with random parameters that are founded in the form of rational, dissipative, explosive, envelope, periodic, and localized soliton can be utilized in fiber applications. The stochastic modulations of structures' amplitude and frequency caused by dramatic instantaneous influences of both fibers nonlinear, dispersive, losing and noise term effects maybe very important in new fiber communications.
- stochastic NLSEs,
- soliton waves,
- explosive,
- envelope,
- solver technique,
- fiber communications
Citation: Yousef F. Alharbi, E. K. El-Shewy, Mahmoud A. E. Abdelrahman. New and effective solitary applications in Schrödinger equation via Brownian motion process with physical coefficients of fiber optics[J]. AIMS Mathematics, 2023, 8(2): 4126-4140. doi: 10.3934/math.2023205

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Abstract

Using the unified solver technique, the rigorous and effective new novel optical progressive and stationary structures are established in the aspects of hyperbolic, trigonometric, rational, periodical and explosive types. These types are concrete in the stochastic nonlinear Schrödinger equations (NLSEs) with operative physical parameters. The obtained stochastic solutions with random parameters that are founded in the form of rational, dissipative, explosive, envelope, periodic, and localized soliton can be utilized in fiber applications. The stochastic modulations of structures' amplitude and frequency caused by dramatic instantaneous influences of both fibers nonlinear, dispersive, losing and noise term effects maybe very important in new fiber communications.

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