Optical soliton perturbation for Gerdjikov–Ivanov equation by extended trial equation method

This paper retrieves Jacobi elliptic, periodic, bright and singular solitons for paraxial nonlinear Schrödinger equation (NLSE) in Kerr media. We use extended trial equation method to obtain these solitons solutions. For the existence of the soliton solutions, constraint conditions are also presented.

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Optical soliton perturbation with full nonlinearity for Gerdjikov–Ivanov equation by trial equation method

Optik ◽

10.1016/j.ijleo.2017.12.099 ◽

2018 ◽

Vol 157 ◽

pp. 1214-1218 ◽

Cited By ~ 28

Author(s):

Anjan Biswas ◽

Yakup Yildirim ◽

Emrullah Yasar ◽

Houria Triki ◽

Ali Saleh Alshomrani ◽

...

Keyword(s):

Optical Soliton ◽

Equation Method ◽

Trial Equation Method ◽

Soliton Perturbation ◽

Full Nonlinearity

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Nematicons in liquid crystals by extended trial equation method

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863517500059 ◽

2017 ◽

Vol 26 (01) ◽

pp. 1750005 ◽

Cited By ~ 50

Author(s):

Mehmet Ekici ◽

Mohammad Mirzazadeh ◽

Abdullah Sonmezoglu ◽

Malik Zaka Ullah ◽

Qin Zhou ◽

...

Keyword(s):

Liquid Crystals ◽

Shock Waves ◽

Governing Equation ◽

Plane Waves ◽

Equation Method ◽

Integration Algorithm ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

First Time ◽

Extended Trial

This paper employs extended trial equation method to retrieve nematicons in liquid crystals from its governing equation. In addition, several other forms of solution naturally emerged from the integration algorithm. These are shock waves, singular solitons, snoidal waves, periodic singular waves, plane waves and others. These variety of solutions are being reported for the first time in the context of liquid crystals.

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Extended Trial Equation Method for Nonlinear Partial Differential Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2014-0345 ◽

2015 ◽

Vol 70 (4) ◽

pp. 269-279 ◽

Cited By ~ 14

Author(s):

Khaled A. Gepreel ◽

Taher A. Nofal

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Equation Method ◽

Hyperbolic Function ◽

Jacobi Elliptic Function ◽

Partial Differential ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

Extended Trial

AbstractThe main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber–Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.

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