Jacobi Elliptic Function Expansion Method for Solving KdV Equation with Conformable Derivative and Dual-Power Law Nonlinearity

Kumar, Vinay; Rezazadeh, Hadi; Eslami, Mostafa; Izadi, Franoosh; Osman, M. S.

doi:10.1007/s40819-019-0710-3

Cited by 79 publications

(15 citation statements)

References 54 publications

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“…It is known that these exact solutions of nonlinear evolution equations (NLEEs), especially the soliton solutions [1][2][3], can be given by using a variety of different methods [4,5], such as Jacobi elliptic function expansion method [6], inverse scattering transformation (IST) [7,8], Darboux transformation (DT) [9], extended generalized DT [10], Lax pair (LP) [11], Lie symmetry analysis [12], Hirota bilinear method [13], and others [14,15]. The Hirota bilinear method is an efficient tool to construct exact solutions of NLEEs, and there exists plenty of completely integrable equations which are studied in this way.…”

Section: Introductionmentioning

confidence: 99%

Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

Jebreen

Chalco-Cano

2021

Advances in Mathematical Physics

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In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2-dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics.

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Section: Introductionmentioning

confidence: 99%

Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

Jebreen

Chalco-Cano

2021

Advances in Mathematical Physics

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“…Studying these models gives more novel properties of them specially by using the computational and numerical schemes. For using most of these schemes, one needs fractional operators to convert the fractional formulas to nonlinear ordinary differential equations with integer order such as Caputo, Caputo-Fabrizio definition, fractional Riemann-Liouville derivatives, conformable fractional derivative, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. These fractional opera-tors have been employed to investigate the exact and numerical solutions of many phenomena.…”

Section: Introductionmentioning

confidence: 99%

The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator

et al. 2020

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Novel explicit wave solutions are constructed for the Kudryashov–Sinelshchikov (KS) equation through liquid–gas bubbles mix under the thermodynamic conditions. A new fractional definition (Atangana–Baleanu derivative operator) is employed through the modified Khater method to get new wave solutions in distinct types of this model that is used to describe the phenomena of pressure waves through liquid–gas bubbles mix under the thermodynamic conditions. The stability property of the obtained solutions is tested to show the ability of our obtained solutions through the physical experiments. The novelty and advantage of the proposed method are illustrated by applying to this model. Some sketches are plotted to show more about the dynamical behavior of this model.

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“…Nonlinear partial differential equations (PDEs) play a significant role in several scientific and engineering fields [1][2][3][4][5]. Since the discovery of the soliton in 1965 by Zabusky and Kruskal [6], many nonlinear PDEs have been derived and extensively applied in different branches of physics and applied mathematics [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

Park

Nuruddeen²,

Ali

et al. 2020

Adv Differ Equ

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This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

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Jacobi Elliptic Function Expansion Method for Solving KdV Equation with Conformable Derivative and Dual-Power Law Nonlinearity

Cited by 79 publications

References 54 publications

Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

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