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

Kaplan, Melike; Akbulut, Arzu

doi:10.1007/s11082-021-03144-y

Cited by 30 publications

(7 citation statements)

References 47 publications

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“…In this study, GKM, which is one of the solution methods of NLEEs, is discussed (Tuluce Demiray, 2020; Tuluce Demiray and Bayrakci, 2021;Pandır and Eren, 2021;Kaplan and Akbulut, 2021;Gurefe, 2020;Islam et al 2019). Firstly, the structure of the method is introduced.…”

Section:  −mentioning

confidence: 99%

New Soliton Solutions Arising in Some NLEEs

BAYRAKCI

Demiray

Yildirim

2022

Bitlis Eren University Journal of Science and Technology

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We have worked on (2+1)-dimensional dissipative long wave system (DLWS) and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation. We have applied GKM, which has been obtained by generalizing the Kudryashov method, to the (2+1)- dimensional DLWS and (2+1)-dimensional DJKM equation. Thus, we have got some new soliton solutions of handled system and equation. We have plotted 2D and 3D surfaces of these acquired results by using Wolfram Mathematica 12. Then, we have shown the validity of the acquired solutions.

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Section:  −mentioning

confidence: 99%

New Soliton Solutions Arising in Some NLEEs

BAYRAKCI

Demiray

Yildirim

2022

Bitlis Eren University Journal of Science and Technology

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“…Let us obtain the exact solutions in the form of solitons. We look for the solution of Equation (12) in the form [47][48][49][50][51]…”

Section: Implicit Optical Solitons Of the Generalized Nonlinear Schrödinger Equationmentioning

confidence: 99%

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Kudryashov

2021

Mathematics

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Application of transformations for dependent and independent variables is used for finding solitary wave solutions of the generalized Schrödinger equations. This new form of equation can be considered as the model for the description of propagation pulse in a nonlinear optics. The method for finding solutions of equation is given in the general case. Solitary waves of equation are obtained as implicit function taking into account the transformation of variables.

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“…The study of exact solutions of such mathematical models is the most exciting area of research investigation. To obtain the exact solutions of such mathematical models, recently, researchers follow different analytical methods, such as tangent hyperbolic method [2], modified extended direct algebraic method [3,4], ðG′/G 2 Þ -expansion method [5], Kudryashov method [6], Lie symmetry method [7], extended trial equation method [8], singular manifold method [9], sinh-Gordon expansion method [10], ðG′/GÞ-expansion method [11], generalized ð G′/GÞ-expansion method [12], generalized-improved ðG′/ GÞ-expansion method [13], extended generalized ðG ′ /GÞ -expansion method [14,15], and ðG′/G, 1/GÞ expansion method [16].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Mohanty

Dev

Sahoo³

et al. 2023

Advances in Mathematical Physics

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In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized G ′ / G expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized G ′ / G expansion technique. The extended generalized G ′ / G expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of G ′ / G . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.

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The analysis of the soliton-type solutions of conformable equations by using generalized 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.

Cited by 30 publications

References 47 publications

New Soliton Solutions Arising in Some NLEEs

New Soliton Solutions Arising in Some NLEEs

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

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The analysis of the soliton-type solutions of conformable equations by using generalized 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.

Cited by 30 publications

References 47 publications

New Soliton Solutions Arising in Some NLEEs

New Soliton Solutions Arising in Some NLEEs

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

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Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method