Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations

Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations

Schrödinger equation is an indispensable model for quantum mechanics, used for modelling several fascinating complex nonlinear physical systems, such as quantum condensates, nonlinear optics, hydrodynamics, shallow-water waves, and the harmonic oscillator. The objective of this paper is to investiga...

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Autor principal: Mohammed Alabedalhadi
Formato: article
Lenguaje:EN
Publicado: Elsevier 2022
Materias:
Traveling wave method
Bäcklund transformation
Fractional Schrödinger equation
Riemann–Liouville derivative
Quantum mechanics
Engineering (General). Civil engineering (General)
TA1-2040
Acceso en línea:https://doaj.org/article/d69acf97527846e191b8a4d8eef4c8f0
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spelling oai:doaj.org-article:d69acf97527846e191b8a4d8eef4c8f02021-11-18T04:45:51ZExact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations1110-016810.1016/j.aej.2021.07.019https://doaj.org/article/d69acf97527846e191b8a4d8eef4c8f02022-02-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S1110016821004889https://doaj.org/toc/1110-0168Schrödinger equation is an indispensable model for quantum mechanics, used for modelling several fascinating complex nonlinear physical systems, such as quantum condensates, nonlinear optics, hydrodynamics, shallow-water waves, and the harmonic oscillator. The objective of this paper is to investigate and study the exact travelling wave solutions of nonlinear triple fractional Schrödinger equations involving a modified Riemann–Liouville fractional derivative. Using the Riccati-Bernoulli Sub-ODE technique, the Bäcklund transformation is employed to handle the posed system. The traveling wave solutions methodology lies in converting the fractional Schrödinger equations into a nonlinear system of fractional ODEs. An infinite sequence of solutions to the fractional partial differential equations can be obtained directly through solving the resulting nonlinear fractional system. Some graphical representations of the obtained solutions after selecting suitable values for fractional values and parameters are illustrated to test accuracy and verify the power, and effectiveness of the proposed method.Mohammed AlabedalhadiElsevierarticleTraveling wave methodBäcklund transformationFractional Schrödinger equationRiemann–Liouville derivativeQuantum mechanicsEngineering (General). Civil engineering (General)TA1-2040ENAlexandria Engineering Journal, Vol 61, Iss 2, Pp 1033-1044 (2022)
institution DOAJ
collection DOAJ
language EN
topic Traveling wave method
Bäcklund transformation
Fractional Schrödinger equation
Riemann–Liouville derivative
Quantum mechanics
Engineering (General). Civil engineering (General)
TA1-2040
spellingShingle Traveling wave method
Bäcklund transformation
Fractional Schrödinger equation
Riemann–Liouville derivative
Quantum mechanics
Engineering (General). Civil engineering (General)
TA1-2040
Mohammed Alabedalhadi
Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
description Schrödinger equation is an indispensable model for quantum mechanics, used for modelling several fascinating complex nonlinear physical systems, such as quantum condensates, nonlinear optics, hydrodynamics, shallow-water waves, and the harmonic oscillator. The objective of this paper is to investigate and study the exact travelling wave solutions of nonlinear triple fractional Schrödinger equations involving a modified Riemann–Liouville fractional derivative. Using the Riccati-Bernoulli Sub-ODE technique, the Bäcklund transformation is employed to handle the posed system. The traveling wave solutions methodology lies in converting the fractional Schrödinger equations into a nonlinear system of fractional ODEs. An infinite sequence of solutions to the fractional partial differential equations can be obtained directly through solving the resulting nonlinear fractional system. Some graphical representations of the obtained solutions after selecting suitable values for fractional values and parameters are illustrated to test accuracy and verify the power, and effectiveness of the proposed method.
format article
author Mohammed Alabedalhadi
author_facet Mohammed Alabedalhadi
author_sort Mohammed Alabedalhadi
title Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
title_short Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
title_full Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
title_fullStr Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
title_full_unstemmed Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
title_sort exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
publisher Elsevier
publishDate 2022
url https://doaj.org/article/d69acf97527846e191b8a4d8eef4c8f0
work_keys_str_mv AT mohammedalabedalhadi exacttravellingwavesolutionsfornonlinearsystemofspatiotemporalfractionalquantummechanicsequations
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