Application of the $(G^{\prime}$ / $G)$ -expansion method for the Burgers, Burgers–Huxley and modified Burgers–KdV equations

“…In this work, we implement the G ′ /G expansion method [29,30,31,32,33] with the help of symbolic computation to derive soliton solution of the Hamiltonian system that reads…”

Section: Preliminariesmentioning

confidence: 99%

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Katatbeh¹,

Abu-Irwaq²,

Alquran³

et al. 2014

Int. J. of Pure and Appl. Math.

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“…Consider the following. The application of the feature equations can be found in [13][14][15][16][17].…”

Section: The Second Type Exact Solutionmentioning

confidence: 99%

Application of the G'/G Expansion Method in Ultrashort Pulses in Nonlinear Optical Fibers

Jiang

Wang

Hua

2013

Advances in Optical Technologies

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With the increasing input power in optical fibers, the dispersion problem is becoming a severe restriction on wavelength division multiplexing (WDM). With the aid of solitons, in which the shape and speed can remain constant during propagation, it is expected that the transmission of nonlinear ultrashort pulses in optical fibers can effectively control the dispersion. The propagation of a nonlinear ultrashort laser pulse in an optical fiber, which fits the high-order nonlinear Schrödinger equation (NLSE), has been solved using the G /G expansion method. Group velocity dispersion, self-phase modulation, the fourth-order dispersion, and the fifth-order nonlinearity of the high-order NLSE were taken into consideration. A series of solutions has been obtained such as the solitary wave solutions of kink, inverse kink, the tangent trigonometric function, and the cotangent trigonometric function. The results have shown that the G /G expansion method is an effective way to obtain the exact solutions for the high-order NLSE, and it provides a theoretical basis for the transmission of ultrashort pulses in nonlinear optical fibers.

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“…Zhang et al [30] devised an algorithm for using the method to solve nonlinear differential difference equations. This method is widely used by the references therein [28,32,33,34,35,36,37,38,39,40,41].…”

Section: Introductionmentioning

confidence: 99%

Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

Kangalgi̇l

2018

int.jour.sci.res.mana

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Abstract:The investigation of the exact solutions of NLPDEs plays an important role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/ G) -expansion method is presented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elementary, effective and can be used for many PDEs in mathematical physics.

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Application of the $(G^{\prime}$ / $G)$ -expansion method for the Burgers, Burgers–Huxley and modified Burgers–KdV equations

Cited by 27 publications

References 20 publications

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Application of the G'/G Expansion Method in Ultrashort Pulses in Nonlinear Optical Fibers

Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

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