Generalized Kudryashov method for nonlinear fractional double sinh--Poisson equation

Demiray, Şeyma Tülüce

doi:10.22436/jnsa.009.03.58

Cited by 21 publications

(8 citation statements)

References 19 publications

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“…In this section, the generalized Kudryashov method will be introduced in detail to obtain the exact solutions of FPDEs defined by Atangana's derivative [31][32][33].…”

Section: The Generalized Kudryashov Methodsmentioning

confidence: 99%

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The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

Gürefe

2020

Rev. Mex. Fís.

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In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger equations defined by Atangana's comformable derivative using the general Kudryashov method. Firstly, Atangana's comformable fractional derivative and its properties are included. Then, by introducing the generalized Kudryashov method, exact solutions of nonlinear fractional partial differential equations (FPDEs), which can be expressed with the comformable derivative of Atangana, are classified. Looking at the results obtained, it is understood that the generalized Kudryashov method can yield important results in obtaining the exact solutions of FPDEs containing beta-derivatives.

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“…In this section, the generalized Kudryashov method will be introduced in detail to obtain the exact solutions of FPDEs defined by Atangana's derivative [31][32][33].…”

Section: The Generalized Kudryashov Methodsmentioning

confidence: 99%

“…In this article, the effectiveness of the generalized Kudryashov method was investigated to determine the exact solutions of the FPDEs with Atangana's conformable derivatives. In some studies in the literature, this method has been applied to various nonlinear fractional problems [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

Gürefe

2020

Rev. Mex. Fís.

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“…In the view of such information, the solutions Eqs. (26), (28) and (30) of Eq. (1) are dark soliton solutions.…”

Section: Physical Explanationmentioning

confidence: 99%

New soliton solutions of the system of equations for the ion sound and Langmuir waves

Demiray

2016

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

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“…Our aim in this article is ascertain the soliton solutions of generalized third-order (NLSE) through GKM (Tuluce Demiray and Bulut, 2015;Pandir et al, 2016;Tuluce Demiray and Bulut, 2016;Tuluce Demiray and Bulut, 2017;Tuluce Demiray and Bulut, 2019). In Section 2, GKM's basic structure is given.…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

Demiray¹,

BAYRAKCI²

2021

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, we have worked on GKM in order to obtain the soliton solutions of the generalized third-order nonlinear Schrödinger equation. Thus, we have acquired some new soliton solutions of the generalized third-order nonlinear Schrödinger equation which has an important usage area in optical fiber. Also, we have drawn some 2D and 3D surfaces of these obtained results by using Wolfram Mathematica 12. Then, we have shown the validity of the obtained solutions.

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Generalized Kudryashov method for nonlinear fractional double sinh--Poisson equation

Abstract: Using the generalized Kudryashov method (GKM), we derive exact solutions of the nonlinear fractional double sinh-Poisson equation. We obtain novel dark soliton solutions. Some numerical simulations were done to see the behavior of these solutions.

Cited by 21 publications

References 19 publications

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

New soliton solutions of the system of equations for the ion sound and Langmuir waves

Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

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