Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity

Khodadad, Farid Samsami; Nazari, Fakhroddin; Eslami, Mostafa; Rezazadeh, Hadi

doi:10.1007/s11082-017-1225-y

Cited by 135 publications

(31 citation statements)

References 38 publications

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“…There are a variety of mathematical procedures that make the study of soliton dynamics possible [31][32][33][34][35] proposed a new methods to address accurate solutions and present conservation laws to this model. Also, A.H. Kara,and others [35] have obtained the Optical soliton solution to this equation using the jacobi elliptic function and (G′/G)-expansion method.…”

Section: Introductionmentioning

confidence: 99%

New Perception of the Optical Solutions to the Fokas-Lenells Equation According to Two Different Techniques

Zahran¹,

Shehata²

2020

Preprint

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In this article, the perturbed Fokas-Lenells equation (FLE)” which plays a vital role in modern asocial media and electronic communication” is employed. Two important different methods are invited to demonstrating new accurate solutions of this equation. The first method is the modified simple equation method (MSEM) that reduces large volume of calculations and realizes closed form solution. While the second is the modified extended tanh-function method (METFM) “which controlled by the auxiliary Ricatti equation” and used effectively to obtain accurate solutions Furthermore, few of the realized results are compatible with that obtained by previous authors elsewhere the others remains new. In addition to the varitional iteration method (VIM )is applied perfectly to achieved the numerical solution corresponding to the exact solution realized by each one of these methods individually.

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Section: Introductionmentioning

confidence: 99%

New Perception of the Optical Solutions to the Fokas-Lenells Equation According to Two Different Techniques

Zahran¹,

Shehata²

2020

Preprint

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“…Another new method for G /G-expansion was studied in [24,25]. A modified ZK equation successfully was obtained by the homogeneous balance method [26] and the Riccati sub-equation technique was used to approximate a Zakharov-Kuznetsov fractional model [27,28]. The first integral method was suggested in [29] for modified KdV-ZK equations.…”

Section: Introductionmentioning

confidence: 99%

A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

et al. 2019

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In this article, an efficient analytical technique, called Laplace-Adomian decomposition method, is used to obtain the solution of fractional Zakharov-Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

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“…This area has drawn the attention of many scientists for more than two decades. Different computational methods have been used to reveal solutions of various type of NLEEs such as the modified exp(−Ψ(η))-expansion function method [7][8][9], the first integral method [10,11], the improved Bernoulli sub-equation function method [12,13], the trial solution method [14,15], the new auxiliary equation method [16], the extended simple equation method [17], the solitary wave ansatz method [18], the functional variable method [19] and several others [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

Sulaıman

2019

Applied Mathematics and Nonlinear Sciences

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This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

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Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity

Cited by 135 publications

References 38 publications

New Perception of the Optical Solutions to the Fokas-Lenells Equation According to Two Different Techniques

New Perception of the Optical Solutions to the Fokas-Lenells Equation According to Two Different Techniques

A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

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