On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations

In this paper, we investigate the equivalence between the Backlund transformation of Riccati equation method and the extended tanh-function method. It is proved that the two methods are equivalent when applying them to partial differential equations and differential-difference equations. Two example...

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Main Authors:	Reham Hassan, Mustafa El-Agamy, Mohamed Soror Abdel Latif, Hamed Nour
Format:	Article
Language:	English
Published:	Ptolemy Scientific Research Press 2020-03-01
Series:	Open Journal of Mathematical Sciences
Subjects:	extended tanh -function method backlund transformation of riccati equation method partial differential equations differential-difference equations.
Online Access:	https://pisrt.org/psr-press/journals/oms-vol-4-2020/on-backlund-transformation-of-riccati-equation-method-and-its-application-to-nonlinear-partial-differential-equations-and-differential-difference-equations/

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spelling	doaj-12e1105b4c4f4a359017b952472cfb7c2020-11-25T02:52:27ZengPtolemy Scientific Research PressOpen Journal of Mathematical Sciences2616-49062523-02122020-03-0141566210.30538/oms2020.0094On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equationsReham Hassan0Mustafa El-Agamy1Mohamed Soror Abdel Latif 2Hamed Nour3Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt.Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt.Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt.Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt.In this paper, we investigate the equivalence between the Backlund transformation of Riccati equation method and the extended tanh-function method. It is proved that the two methods are equivalent when applying them to partial differential equations and differential-difference equations. Two examples are introduced to justify our results.https://pisrt.org/psr-press/journals/oms-vol-4-2020/on-backlund-transformation-of-riccati-equation-method-and-its-application-to-nonlinear-partial-differential-equations-and-differential-difference-equations/extended tanh -function methodbacklund transformation of riccati equation methodpartial differential equationsdifferential-difference equations.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Reham Hassan Mustafa El-Agamy Mohamed Soror Abdel Latif Hamed Nour
spellingShingle	Reham Hassan Mustafa El-Agamy Mohamed Soror Abdel Latif Hamed Nour On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations Open Journal of Mathematical Sciences extended tanh -function method backlund transformation of riccati equation method partial differential equations differential-difference equations.
author_facet	Reham Hassan Mustafa El-Agamy Mohamed Soror Abdel Latif Hamed Nour
author_sort	Reham Hassan
title	On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
title_short	On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
title_full	On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
title_fullStr	On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
title_full_unstemmed	On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
title_sort	on backlund transformation of riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
publisher	Ptolemy Scientific Research Press
series	Open Journal of Mathematical Sciences
issn	2616-4906 2523-0212
publishDate	2020-03-01
description	In this paper, we investigate the equivalence between the Backlund transformation of Riccati equation method and the extended tanh-function method. It is proved that the two methods are equivalent when applying them to partial differential equations and differential-difference equations. Two examples are introduced to justify our results.
topic	extended tanh -function method backlund transformation of riccati equation method partial differential equations differential-difference equations.
url	https://pisrt.org/psr-press/journals/oms-vol-4-2020/on-backlund-transformation-of-riccati-equation-method-and-its-application-to-nonlinear-partial-differential-equations-and-differential-difference-equations/
work_keys_str_mv	AT rehamhassan onbacklundtransformationofriccatiequationmethodanditsapplicationtononlinearpartialdifferentialequationsanddifferentialdifferenceequations AT mustafaelagamy onbacklundtransformationofriccatiequationmethodanditsapplicationtononlinearpartialdifferentialequationsanddifferentialdifferenceequations AT mohamedsororabdellatif onbacklundtransformationofriccatiequationmethodanditsapplicationtononlinearpartialdifferentialequationsanddifferentialdifferenceequations AT hamednour onbacklundtransformationofriccatiequationmethodanditsapplicationtononlinearpartialdifferentialequationsanddifferentialdifferenceequations
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On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations

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