scholarly journals The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method

2021 ◽  
Author(s):  
Melike Kaplan ◽  
Arzu Akbulut
Keyword(s):  
Burgers Equation ◽  
Conformable Derivative ◽  
Research Article ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

Abstract This research article is dedicated to applying the generalized Kudryashov method in order to acquire new exact and soliton-type solutions of the conformable Burgers' equation and Wu-Zhang system with conformable derivative.

scholarly journals Generalized Kudryashov Method for Time-Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Yusuf Pandir ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Third Order ◽  
Hilliard Equation ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Cahn Hilliard Equation

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

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

2016 ◽  
Vol 7 (1) ◽  
pp. 42-49
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Sound Wave ◽  
High Frequency ◽  
Ponderomotive Force ◽  
Soliton Solutions ◽  
Langmuir Wave ◽  
Dark Soliton ◽  
System Of Equations ◽  
Langmuir Waves ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

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.

Shock Waves, Variational Principle and Conservation Laws of a Schamel–Zakharov–Kuznetsov–Burgers Equation in a Magnetised Dust Plasma

2018 ◽  
Vol 73 (8) ◽  
pp. 693-704 ◽  
Author(s):  
O.H. EL-Kalaawy ◽  
Engy A. Ahmed
Keyword(s):  
Variational Principle ◽  
Conservation Laws ◽  
Acoustic Waves ◽  
Burgers Equation ◽  
Special Functions ◽  
Nonlinear Propagation ◽  
Ion Acoustic Waves ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Plasma Dust

AbstractIn this article, we investigate a (3+1)-dimensional Schamel–Zakharov–Kuznetsov–Burgers (SZKB) equation, which describes the nonlinear plasma-dust ion acoustic waves (DIAWs) in a magnetised dusty plasma. With the aid of the Kudryashov method and symbolic computation, a set of new exact solutions for the SZKB equation are derived. By introducing two special functions, a variational principle of the SZKB equation is obtained. Conservation laws of the SZKB equation are obtained by two different approaches: Lie point symmetry and the multiplier method. Thus, the conservation laws here can be useful in enhancing the understanding of nonlinear propagation of small amplitude electrostatic structures in the dense, dissipative DIAWs’ magnetoplasmas. The properties of the shock wave solutions structures are analysed numerically with the system parameters. In addition, the electric field of this solution is investigated. Finally, we will study the physical meanings of solutions.

scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

scholarly journals A short review on analytical methods for fractional equations with he’s fractional derivative

2017 ◽  
Vol 21 (4) ◽  
pp. 1567-1574 ◽  
Author(s):  
Yan Wang ◽  
Yu-Feng Zhang ◽  
Jian-Gen Liu ◽  
Muhammad Iqbal
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Methods ◽  
Function Method ◽  
Solution Process ◽  
Short Review ◽  
Fractional Equations ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Fractional Differential

He?s fractional derivative is adopted in this paper, and analytical methods for fractional differential equations are briefly reviewed, two modifications of the exp-function method (the generalized Kudryashov method and generalized expo-nential rational function method) are emphasized, and fractional Benjamin-Bo-na-Mahony equation with He?s fractional derivative is used as an example to elucidate the solution process.

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