Optical soliton solutions for the variable coefficient modified Kawahara equation

Bekir, Ahmet; Güner, Özkan; Bilgil, Halis

doi:10.1016/j.ijleo.2015.06.051

Cited by 11 publications

(4 citation statements)

References 36 publications

(35 reference statements)

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“…When this method was successfully extended to fractional calculus [48] by He in 2013, it became an effective tool for fractional differential equations, see Refs. [49][50][51][52].…”

Section: Exp-function Methodsmentioning

confidence: 99%

Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation

Güner¹

2017

Commun. Theor. Phys.

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In the present article, He’s fractional derivative, the ansatz method, the (G′/G)-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM). As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations (FDEs) and it can be applied to other nonlinear FDEs.

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“…When this method was successfully extended to fractional calculus [48] by He in 2013, it became an effective tool for fractional differential equations, see Refs. [49][50][51][52].…”

Section: Exp-function Methodsmentioning

confidence: 99%

Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation

Güner¹

2017

Commun. Theor. Phys.

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“…When considering Equations (45) along with (8) in (31) for u px, y, tq and in Equation (23) for v px, y, tq, another new hyperbolic function solution to the DLW system(1) can be obtained as the following, under the condition of Family-1; λ 2´4 µ ą 0:…”

Section: Case-2mentioning

confidence: 99%

“…One of them is to obtain various solutions of coastal, oceans and fluid problems such as approximate, numerical, analytical and traveling wave solutions. Some important traveling wave solutions for nonlinear differential equations have been investigated by different authors [8][9][10][11][12][13][14][15]. In the rest of this manuscript; we have explained the fundamental properties of the modified exp(´Ω(ξ))-expansion function method (MEFM) and Improved Bernoulli sub-equation function method (IBSEFM) in Section 2.…”

Section: Introductionmentioning

confidence: 99%

New Complex Hyperbolic Function Solutions for the (2+1)-Dimensional Dispersive Long Water–Wave System

Baskonus

2016

MCA

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Abstract:In this paper, new algorithms called the "Modified exp(´Ω)-expansion function method" and "Improved Bernoulli sub-equation function method" have been proposed. The first algorithm is based on the exp(´Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The analytical solutions and application results are presented by drawing the two-and three-dimensional surfaces of solutions such as hyperbolic, complex, trigonometric and exponential solutions for the (2+1)-dimensional dispersive long water-wave system. Finally, a conclusion has been presented by mentioning the important discoveries in this manuscript.

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“…Solitons which are self-reinforcing solitary wave packets are one of the most important areas of research in the field of nonlinear optics. [1] Therefore, an important problem is obtaining solutions of these equations. In the last three decades, many methods were developed for constructing the analytical solutions of NLEEs.…”

Section: Introductionmentioning

confidence: 99%

Multiple exp-function method for soliton solutions of nonlinear evolution equations

Yıldırım

Yaşar

2017

Chinese Phys. B

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We applied the multiple exp-function scheme to the (2+1)-dimensional Sawada-Kotera (SK) equation and (3+1)dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.

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Optical soliton solutions for the variable coefficient modified Kawahara equation

Cited by 11 publications

References 36 publications

Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation

Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation

New Complex Hyperbolic Function Solutions for the (2+1)-Dimensional Dispersive Long Water–Wave System

Multiple exp-function method for soliton solutions of nonlinear evolution equations

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