Impacts of Brownian motion and fractional derivative on the solutions of the stochastic fractional Davey-Stewartson equations

Mohammed, Wael W.; Al‐Askar, Farah M.; El-Morshedy, Mahmoud

doi:10.1515/dema-2022-0233

Cited by 4 publications

(2 citation statements)

References 35 publications

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“…Next, let us add Equations ( 32) and (33). After some straightforward simplifications, we readily reach that…”

Section: Resultsmentioning

confidence: 99%

“…For instance, a study explored the impacts of Brownian motion and fractional derivatives on the solutions of the stochastic fractional DSS. Some authors used two different approaches, namely, the Riccati-Bernoulli sub-ordinary differential equations and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, and rational stochastic solutions [33]. In another study, a new iterative method was proposed to solve fractional DSS [34].…”

Section: Mathematical Modelmentioning

confidence: 99%

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Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Molina-Holguín,

Urenda-Cázares,

Macías-Díaz

et al. 2024

Fractal Fract

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In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz type, and extensions of the classical mass, energy, and momentum operators will be proposed in the fractional-case scenario. In this work, we will prove rigorously that these functionals are conserved throughout time using some functional properties of the Riesz fractional operators. This study is intended to serve as a stepping stone for further exploration of the generalized Davey–Stewartson system and its wide-ranging applications.

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“…Next, let us add Equations ( 32) and (33). After some straightforward simplifications, we readily reach that…”

Section: Resultsmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Molina-Holguín,

Urenda-Cázares,

Macías-Díaz

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

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Retrieval of optical soliton solutions of stochastic perturbed Schrödinger-Hirota equation with Kerr law in the presence of spatio-temporal dispersion

Ozisik,

Secer,

Bayram

2023

Opt Quant Electron

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Optical Soliton solutions for stochastic Davey–Stewartson equation under the effect of noise

Iqbal,

Inc

2024

Opt Quant Electron

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In this manuscript, we investigates the stochastic Davey–Stewartson equation under the influence of noise in It$${\hat{o}}$$ o ^ sense. This equations is a two-dimensional integrable equations, are higher-dimensional variations of the nonlinear Schrödinger equation. Plasma physics, nonlinear optics, hydrodynamics, and other fields have made use of the solutions to the stochastic Davey–Stewartson equations. The Sardar subequation method is used that will gives us the the stochastic optical soliton solutions in the form of dark, bright, combine and periodic waves. These exact optical soliton solutions are helpful in understanding a variety of fascinating physical phenomena because of the importance of the Davey- Stewartson equations in the theory of turbulence for plasma waves or in optical fibers. Additionally, we use Mathematica tools to plot our solutions and exhibit a series of three-dimensional, two-dimensional and their corresponding contour graphs to show how the noise affects the exact solutions of the stochastic Davey–Stewartson equation. We show how the stochastic Davey–Stewartson solutions are stabilised at around zero by the multiplicative Brownian motion.

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Impacts of Brownian motion and fractional derivative on the solutions of the stochastic fractional Davey-Stewartson equations

Cited by 4 publications

References 35 publications

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Retrieval of optical soliton solutions of stochastic perturbed Schrödinger-Hirota equation with Kerr law in the presence of spatio-temporal dispersion

Optical Soliton solutions for stochastic Davey–Stewartson equation under the effect of noise

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