Exact solutions of the stochastic Maccari system forced by multiplicative noise

Al‐Askar, Farah M.; Mohammed, Wael W.; Aly, E. S.; Elmorshedy, Mahmoud F.

doi:10.1002/zamm.202100199

Cited by 12 publications

(4 citation statements)

References 33 publications

(54 reference statements)

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“…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

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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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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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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,

Rahman

2024

Preprint

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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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“…The use of stochastic NEEs for developing mathematical models of complex processes is on the rise in many fields, including materials sciences, condensed matter climate, finance, information systems, electrical engineering, biophysics and physics system modeling [14,15]. In recent years, analytical solutions for some stochastic NEEs have been acquired, for example [16][17][18][19][20] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise

2023

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We study the (3+1)-dimensional stochastic Jimbo–Miwa (SJM) equation induced by multiplicative white noise in the Itô sense. We employ the Riccati equation mapping and He’s semi-inverse techniques to provide trigonometric, hyperbolic, and rational function solutions of SJME. Due to the applications of the Jimbo–Miwa equation in ocean studies and other disciplines, the acquired solutions may explain numerous fascinating physical phenomena. Using a variety of 2D and 3D diagrams, we illustrate how white noise influences the analytical solutions of SJM equation. We deduce that the noise destroys the symmetry of the solutions of SJM equation and stabilizes them at zero.

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Exact solutions of the stochastic Maccari system forced by multiplicative noise

Cited by 12 publications

References 33 publications

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

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

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

The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise

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