The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation

Al‐Askar, Farah M.; Cesarano, Clemente; Mohammed, Wael W.

doi:10.3390/axioms12050447

Cited by 13 publications

(5 citation statements)

References 29 publications

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“…The stochastic wave transform is now used to obtain the exact solitary wave solutions for the stochastic biofilm system (3)-( 4), such as [25,30,31]:…”

Section: Stochastic Exact Solutionsmentioning

confidence: 99%

Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing

Baber,

Ahmed,

Yasin

et al. 2024

Mathematics

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This study deals with a stochastic reaction–diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development and decomposition of the biofilm, and the biofilm bacteria collaboration, which demonstrates the potency of resistance and defense against environmental stimuli. In this study, we investigate numerical solutions and exact solitary wave solutions with the presence of randomness. The finite difference scheme is proposed for the sake of numerical solutions while the generalized Riccati equation mapping method is applied to construct exact solitary wave solutions. The numerical scheme is analyzed by checking consistency and stability. The consistency of the scheme is gained under the mean square sense while the stability condition is gained by the help of the Von Neumann criteria. Exact stochastic solitary wave solutions are constructed in the form of hyperbolic, trigonometric, and rational forms. Some solutions are plots in 3D and 2D form to show dark, bright and solitary wave solutions and the effects of noise as well. Mainly, the numerical results are compared with the exact solitary wave solutions with the help of unique physical problems. The comparison plots are dispatched in three dimensions and line representations as well as by selecting different values of parameters.

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“…The stochastic wave transform is now used to obtain the exact solitary wave solutions for the stochastic biofilm system (3)-( 4), such as [25,30,31]:…”

Section: Stochastic Exact Solutionsmentioning

confidence: 99%

Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing

Baber,

Ahmed,

Yasin

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…These recent advancements mark a notable breakthrough in the field, as researchers have successfully obtained exact solutions for a subset of SDEs. The exploration of exact solutions in the realm of SDEs continues to enhance our knowledge and pave the way for further advancements in stochastic analysis and related disciplines [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Novel stochastic multi breather type, a-periodic, hybrid periodic and other type of waves of the Shrödinger–Hirota model with Wiener process

Al-Essa,

ur Rahman

2024

Opt Quant Electron

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The current manuscript elaborate a novel characteristic of stochastic multi breather type, periodic, hybrid periodic and different type of waves solutions for the Shrödinger-Hirota (SH) equation.The mentioned equation is studied by a Wiener process and white noise which is used for the sudden and large-scale fluctuation. By applying the wave transformation technique the considered equation is transformed into ordinary differential equations, gives meaningful analysis. From the solution of the SH equation various type of results, including soliton, dark, bright, hybrid and periodic solitons. To visually capture these intricate behaviors, we employ MATLAB tools to generate 2D and 3D graphs of the analytical stochastic solutions. This combination of mathematical rigor and numerical simulations provides a comprehensive understanding of the phenomena under study, making a valuable contribution to the field of nonlinear wave equations and stochastic processes.

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“…It is crucial to investigate the exact explicit solutions of NLEEs in order to gain a deeper understanding of the phenomena described by NLEEs. In recent years, quite a few techniques, including the first-integral method [1], sine-cosine procedure [2], exp-function method [3], Jacobi elliptic function expansion [4], mapping method [5], auxiliary equation scheme [6], extended tanh function method [7], generalized Kudryashov approach [8], exp(−φ(ς))-expansion method [9], F-expansion approach [10], Taylor's power series expansion [11], q-homotopy analysis transform method [12], bifurcation analysis [13,14], and (G /G)-expansion [15,16], have been proposed for solving NLEEs. Moreover, the Lie symmetry method [17] is the most significant method for developing analytical solutions for nonlinear NLEEs.…”

Section: Introductionmentioning

confidence: 99%

Solitary Solutions for the Stochastic Fokas System Found in Monomode Optical Fibers

2023

Self Cite

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The stochastic Fokas system (SFS), driven by multiplicative noise in the Itô sense, was investigated in this study. Novel trigonometric, rational, hyperbolic, and elliptic stochastic solutions are found using a modified mapping method. Because the Fokas system is used to explain nonlinear pulse propagation in monomode optical fibers, the solutions provided may be utilized to analyze a broad range of critical physical phenomena. In order to explain the impacts of multiplicative noise, the dynamic performances of the different found solutions are illustrated using 3D and 2D curves. We conclude that multiplicative noise eliminates the symmetry of the solutions of the SFS and stabilizes them.

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The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation

Cited by 13 publications

References 29 publications

Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing

Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing

Novel stochastic multi breather type, a-periodic, hybrid periodic and other type of waves of the Shrödinger–Hirota model with Wiener process

Solitary Solutions for the Stochastic Fokas System Found in Monomode Optical Fibers

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