A generalized Kudryashov method to some nonlinear evolution equations in mathematical physics

Kaplan, Melike; Bekir, Ahmet; Akbulut, Arzu

doi:10.1007/s11071-016-2867-1

Cited by 131 publications

(47 citation statements)

References 43 publications

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“…1, 2, we plot 2D and 3D surfaces of q 1 ( ) and r 1 ( ) in Eq. (15), which explain the vitality of solutions with appropriate parameters. In Figs.…”

Section: Resultsmentioning

confidence: 99%

Constructing new wave solutions to the $$(2 + 1)$$-dimensional Davey–Stewartson equation (DSE) which arises in fluid dynamics

Achab

2019

JMST Adv.

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In this paper, we utilize the uniform algebraic method and construct some new wave solutions to the (2 + 1)-dimensional Davey-Stewartson equation which arises in fluid dynamics. We successfully obtain some hyperbolic and trigonometric function solutions to this equation. Subsequently, We have also built the Lagrangian and the Hamiltonian for the second-order nonlinear ODE corresponding to the traveling wave reduction of the (DSE)-equation. Moreover, we plot 2D and 3D surfaces representing the obtained solutions by considering some suitable values of the parameters. The unique (2 + 1)-dimensional dynamics of the obtained exact solutions of the (DSE) equation may help to understand the formation and key properties of traveling waves in many other physical settings. Before the end of this paper, we compare our results with the existing results in the literature by presenting comprehensive conclusions.

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“…1, 2, we plot 2D and 3D surfaces of q 1 ( ) and r 1 ( ) in Eq. (15), which explain the vitality of solutions with appropriate parameters. In Figs.…”

Section: Resultsmentioning

confidence: 99%

Constructing new wave solutions to the $$(2 + 1)$$-dimensional Davey–Stewartson equation (DSE) which arises in fluid dynamics

Achab

2019

JMST Adv.

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“…More details can be seen in Refs. (Ryabov et al, 2011;Kabir et al, 2011;Kudryashov, 2012;Mirzazadeh, 2014;Kaplan, 2016).…”

Section: Kudryashov Methods For Npdementioning

confidence: 99%

“…Therefore, these methods have an important place in science. Some of these developed methods are as follows: Homotopy Perturbation Method He (2000), Adomian Decomposition Method Bildik et al (2006), (G'/ G, 1/ G) -expansion method Daghan and Dönmez (2016) and Kudryashov Method (Ryabov et al, 2011;Kabir et al, 2011;Kudryashov, 2012;Mirzazadeh, 2014;Kaplan, 2016).…”

Section: Introductionmentioning

confidence: 99%

Application of Kudryashov Method to Some Equations Used in Physics Science

Yıldız

2019

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, Kudryashov Method is used to find the wave solutions of the Gardner equation, fifth order Caudrey-Dodd-Gibbon equation and Sawada-Kotera equation, which are non-linear partial differential equations used as a mathematical model in the physics science field and engineering applications. The exact solutions obtained are compared with the results in the literature and hyperbolic type and soliton solutions are obtained.

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“…For example, the homogeneous balance method [21], the tanh method [22], the Jacobi elliptic function expansion [23][24][25][26], the truncated Painlevé expansion [27], differential quadrature method [28], Hirota bilinear method [29], Darboux transformations [30], the trial equation method [31]. Seadawy et al [32] proposed the sech-tanh method to solve the Olver equation and the fifth-order KdV equation and obtained traveling wave solutions; in [33][34][35][36][37][38] was introduced a method called the G G -expansion method and one obtained a traveling solution for the four well established nonlinear evolution equations. In [5], the authors obtained traveling wave solutions for the generalized Camassa-Holm equation by polynomial expansion methods.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, on the basis of the G G -expansion method [5,[33][34][35][36][37][38], we use the solutions of the Riccati equation [39] to extend the auxiliary equation G + λG + μG = 0 and obtain more exact solutions of the auxiliary equation [40], thus we derive more new exact solutions of Eq. (1.1).…”

Section: Introductionmentioning

confidence: 99%

New exact solutions for Kudryashov–Sinelshchikov equation

Lü

2018

Adv Differ Equ

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In this paper, we firstly change the auxiliary second order ordinary differential equation in the G G-polynomial expansion method to the Riccati equation. By solving the Riccati equation, we obtain more exact solutions to the auxiliary equation and thus obtain more new exact solutions to the Kudryashov-Sinelshchikov equation, which mainly include three types of solutions with parameters: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At last, some examples and figures are given to demonstrate the solutions.

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A generalized Kudryashov method to some nonlinear evolution equations in mathematical physics

Cited by 131 publications

References 43 publications

Constructing new wave solutions to the $$(2 + 1)$$-dimensional Davey–Stewartson equation (DSE) which arises in fluid dynamics

Constructing new wave solutions to the $$(2 + 1)$$-dimensional Davey–Stewartson equation (DSE) which arises in fluid dynamics

Application of Kudryashov Method to Some Equations Used in Physics Science

New exact solutions for Kudryashov–Sinelshchikov equation

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