New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity

Rezazadeh, Hadi

doi:10.1016/j.ijleo.2018.04.026

Cited by 290 publications

(77 citation statements)

References 21 publications

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“…Seeking different types of solutions to FDEs for such phenomena has become the subject of interest for researchers. Thus, a lot of powerful mathematical methods have been applied to obtain exact analytic solutions of FDEs, namely, the extended tanh-function method [6,7], the exp-function method [8,9], the sub-equation method [10,11], the improved tan(φ /2)-expansion method [12,13], the (G /G)-expansion method [14,15], the modified trial equation method [16,17], the new extended direct algebraic method [18,19], the extended sinh-Gordon equation expansion method [20,21], the unified method [22] and so on.…”

Section: Introductionmentioning

confidence: 99%

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Al-Ghafri

Rezazadeh

2019

Applied Mathematics and Nonlinear Sciences

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In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.

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Section: Introductionmentioning

confidence: 99%

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Al-Ghafri

Rezazadeh

2019

Applied Mathematics and Nonlinear Sciences

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“…In addition to these advantages CFD is type of local fractional derivatives are important in themselves being used, due to their well-behaved, in generalizing and describing certain models depending on ordinary or partial differential equations [6,7,14,[18][19][20][21][22][23][24]. Exact solutions can be obtained.…”

Section: Definition 12mentioning

confidence: 99%

Exact solutions of fractional partial differential equation systems with conformable derivative

Özkan

Kurt

2019

Filomat

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Main goal of this paper is to have the new exact solutions of some fractional partial differential equation systems (FPDES) in conformable sense. The definition of conformable fractional derivative (CFD) is similar to the limit based definition of known derivative. This derivative obeys both rules which other popular derivatives do not satisfy such as derivative of the quotient of two functions, the derivative product of two functions, chain rule and etc. By using conformable derivative it is seen that the solution procedure for (PDES) is simpler and more efficient.1. The Riemann-Liouville derivative of a constant do not equal to zero (Caputo derivative satisfies).

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“…Note that the travelling wave reduction of the GL model (1) is obtained by taking ν = 2 in all previous studies [26][27][28][29][30][31][32][33][34][35][36][37][38]. Then, the analytic exact solution is extracted by applying various integration schemes (first integral method, semi-inverse variational principle, G /G method, exp-function method, Riccati equation method, simplest equation method, trial solution approach, etc.).…”

Section: Introductionmentioning

confidence: 99%

Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

Al-Ghafri

2020

Symmetry

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In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.

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New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity

Cited by 290 publications

References 21 publications

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Exact solutions of fractional partial differential equation systems with conformable derivative

Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

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