Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

This work is devoted to providing new kinds of deterministic and stochastic solutions of one of the famous nonlinear equations that depends on time, called the Schrödinger–Hirota equation. A new and straightforward methodology is offered to extract exact wave solutions of the stochastic nonlinear ev...

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Autores principales:	Abd-Allah Hyder, Ahmed H. Soliman, Clemente Cesarano, M. A. Barakat
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Schrödinger–Hirota equation conformable factor effect generalized Kudryashov scheme extended stochastic models exact solutions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c9a6500e3e0f489993a72bdddd724e65
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spelling	oai:doaj.org-article:c9a6500e3e0f489993a72bdddd724e652021-11-11T18:18:15ZSolving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type10.3390/math92127602227-7390https://doaj.org/article/c9a6500e3e0f489993a72bdddd724e652021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2760https://doaj.org/toc/2227-7390This work is devoted to providing new kinds of deterministic and stochastic solutions of one of the famous nonlinear equations that depends on time, called the Schrödinger–Hirota equation. A new and straightforward methodology is offered to extract exact wave solutions of the stochastic nonlinear evolution equations (NEEs) with generalized differential conformable operators (GDCOs). This methodology combines the features of GDCOs, some instruments of white noise analysis, and the generalized Kudryashov scheme. To demonstrate the usefulness and validity of our methodology, we applied it to extract diversified exact wave solutions of the Schrödinger–Hirota equation, particularly in a Wick-type stochastic space and with GDCOs. These wave solutions can be turned into soliton and periodic wave solutions that play a main role in numerous fields of nonlinear physical sciences. Moreover, three-dimensional, contour, and two-dimensional graphical visualizations of some of the extracted solutions are exhibited with some elected functions and parameters. According to the results, our new approach demonstrates the impact of random and conformable factors on the solutions of the Schrödinger–Hirota equation. These findings can be applied to build new models in plasma physics, condensed matter physics, industrial studies, and optical fibers. Furthermore, to reinforce the importance of the acquired solutions, comparative aspects connected to some former works are presented for these types of solutions.Abd-Allah HyderAhmed H. SolimanClemente CesaranoM. A. BarakatMDPI AGarticleSchrödinger–Hirota equationconformable factor effectgeneralized Kudryashov schemeextended stochastic modelsexact solutionsMathematicsQA1-939ENMathematics, Vol 9, Iss 2760, p 2760 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Schrödinger–Hirota equation conformable factor effect generalized Kudryashov scheme extended stochastic models exact solutions Mathematics QA1-939
spellingShingle	Schrödinger–Hirota equation conformable factor effect generalized Kudryashov scheme extended stochastic models exact solutions Mathematics QA1-939 Abd-Allah Hyder Ahmed H. Soliman Clemente Cesarano M. A. Barakat Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type
description	This work is devoted to providing new kinds of deterministic and stochastic solutions of one of the famous nonlinear equations that depends on time, called the Schrödinger–Hirota equation. A new and straightforward methodology is offered to extract exact wave solutions of the stochastic nonlinear evolution equations (NEEs) with generalized differential conformable operators (GDCOs). This methodology combines the features of GDCOs, some instruments of white noise analysis, and the generalized Kudryashov scheme. To demonstrate the usefulness and validity of our methodology, we applied it to extract diversified exact wave solutions of the Schrödinger–Hirota equation, particularly in a Wick-type stochastic space and with GDCOs. These wave solutions can be turned into soliton and periodic wave solutions that play a main role in numerous fields of nonlinear physical sciences. Moreover, three-dimensional, contour, and two-dimensional graphical visualizations of some of the extracted solutions are exhibited with some elected functions and parameters. According to the results, our new approach demonstrates the impact of random and conformable factors on the solutions of the Schrödinger–Hirota equation. These findings can be applied to build new models in plasma physics, condensed matter physics, industrial studies, and optical fibers. Furthermore, to reinforce the importance of the acquired solutions, comparative aspects connected to some former works are presented for these types of solutions.
format	article
author	Abd-Allah Hyder Ahmed H. Soliman Clemente Cesarano M. A. Barakat
author_facet	Abd-Allah Hyder Ahmed H. Soliman Clemente Cesarano M. A. Barakat
author_sort	Abd-Allah Hyder
title	Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type
title_short	Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type
title_full	Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type
title_fullStr	Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type
title_full_unstemmed	Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type
title_sort	solving schrödinger–hirota equation in a stochastic environment and utilizing generalized derivatives of the conformable type
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c9a6500e3e0f489993a72bdddd724e65
work_keys_str_mv	AT abdallahhyder solvingschrodingerhirotaequationinastochasticenvironmentandutilizinggeneralizedderivativesoftheconformabletype AT ahmedhsoliman solvingschrodingerhirotaequationinastochasticenvironmentandutilizinggeneralizedderivativesoftheconformabletype AT clementecesarano solvingschrodingerhirotaequationinastochasticenvironmentandutilizinggeneralizedderivativesoftheconformabletype AT mabarakat solvingschrodingerhirotaequationinastochasticenvironmentandutilizinggeneralizedderivativesoftheconformabletype
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Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

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