Application of Modified Extended Tanh Technique for solving Complex Ginzburg-Landau Equation considering Kerr Law Nonlinearity

Chu, Yu‐Ming; Shallal, Muhannad A.; Mirhosseini-Alizamini, Seyed Mehdi; Rezazadeh, Hadi; Javeed, Shumaila; Băleanu, Dumitru

doi:10.32604/cmc.2020.012611

Cited by 21 publications

(8 citation statements)

References 15 publications

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“…They all described the methods in detail and obtained many remarkable results. This can be seen in previous studies 26–40 . For example, in the literature, 33 Zayed and Alurr used the extended auxiliary equation method to solve the soliton solution of the following equation:

i u_{t} + a u_{x x} + false(b false| u {false|}^{2} + c false| u {false|}^{4} false) u + d false(\frac{{false(false| u false| false)}_{x x}}{false| u false|} false) u = 0,

where u = u ( x , t ) is a complex function that represents a normalized complex amplitude of the pulse envelope in nonlinear optical fiber.…”

Section: Introductionmentioning

confidence: 91%

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Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

Wang

Zhang

Essel

2022

Math Methods in App Sciences

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In this paper, we define different ansatz equations to study two classes of high‐order nonlinear Schrödinger equations. The concrete forms of soliton solutions of these two classes of equations are obtained by using this equation. This paper briefly summarizes and explains the method used and applies it to two classes of specific equations. Finally, the concrete form of solutions and the necessary conditions for the existence of solutions are obtained, and pictures are added to assist understanding.

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i u_{t} + a u_{x x} + false(b false| u {false|}^{2} + c false| u {false|}^{4} false) u + d false(\frac{{false(false| u false| false)}_{x x}}{false| u false|} false) u = 0,

where u = u ( x , t ) is a complex function that represents a normalized complex amplitude of the pulse envelope in nonlinear optical fiber.…”

Section: Introductionmentioning

confidence: 91%

“…This can be seen in previous studies. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] For example, in the literature, 33 Zayed and Alurr used the extended auxiliary equation method to solve the soliton solution of the following equation:…”

Section: Introductionmentioning

confidence: 99%

Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

Wang

Zhang

Essel

2022

Math Methods in App Sciences

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“…Substituting the phase-amplitude decomposition into Eq. ( 4) results in the following couple of equations after breaking into real and imaginary parts [33,34]:…”

Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

“…Many researchers have recently solved the CGLE. Chu et al [33] have solved this equation with the help of modified extended tanh technique and received different forms of solitons, such as, hyperbolic and trigonometric functions. The modified simple equation method is used to obtain some bright, dark and singular soliton solutions by Arnous and Ahmed [34].…”

Section: Introductionmentioning

confidence: 99%

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

Isah

Yokuş

2022

mmnsa

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This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The ϕ 6 -model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

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“…The presented model can be extended in view of fractional calculus (FC) as given in Refs 26–29,31–33 . The last but not the least the reader can refer to the Refs 34–40 . for recently published articles in the related topics.…”

Section: Introductionmentioning

confidence: 99%

A new perspective for the numerical solution of the Modified Equal Width wave equation

Başhan

Yağmurlu

Uçar

et al. 2021

Math Methods in App Sciences

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Finding the approximate solutions to natural systems in the branch of mathematical modelling has become increasingly important and for this end various methods have been proposed. The purpose of the present paper is to obtain and analyze the numerical solutions of Modified Equal Width equation (MEW). This equation is one of those equations used to model nonlinear phenomena which has a significant role in several branches of science such as plasma physics, fluid mechanics, optics and kinetics. Firstly, for the discretization of spatial derivatives, a fifth‐order quintic B‐spline based scheme is directly implemented. Secondly, a forward finite difference formula is applied for the temporal discretization of derivatives with respect to time. Simulation results establish the validity and applicability of the suggested technique for a wide range of nonlinear equations. Then, the newly obtained theoretical consequences are numerically justified by the simulations and test problems. These illustrative test problems are presented verifying the superiority of the newly presented scheme compared to other existing schemes and techniques. The suggested method with symbolic computational software such as, Matlab, is proven as an effective way to obtain the soliton solutions of several nonlinear partial differential equations (PDEs). Finally, the newly obtained results are presented graphically to justify the approximate findings.

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Application of Modified Extended Tanh Technique for solving Complex Ginzburg-Landau Equation considering Kerr Law Nonlinearity

Cited by 21 publications

References 15 publications

Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

A new perspective for the numerical solution of the Modified Equal Width wave equation

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