scholarly journals Extended trial equation method for nonlinear coupled Schrodinger Boussinesq partial differential equations

2016 ◽  
Vol 24 (3) ◽  
pp. 381-391 ◽  
Author(s):  
Khaled A. Gepreel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Equation Method ◽  
Partial Differential ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Extended Trial

Extended Trial Equation Method for Nonlinear Partial Differential Equations

2015 ◽  
Vol 70 (4) ◽  
pp. 269-279 ◽  
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.

scholarly journals The Extended Trial Equation Method for Some Time Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yusuf Pandir ◽  
Yusuf Gurefe ◽  
Emine Misirli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Equation Method ◽  
Wave Transformation ◽  
Jacobi Elliptic Function ◽  
Partial Differential ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Liouville Derivative ◽  
Extended Trial

Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractionalKn,nequation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions.

Optical solitons in DWDM system by extended trial equation method

Optik ◽  
2017 ◽  
Vol 141 ◽  
pp. 157-167 ◽  
Author(s):  
Mehmet Ekici ◽  
Abdullah Sonmezoglu ◽  
Qin Zhou ◽  
Anjan Biswas ◽  
Malik Zaka Ullah ◽  
...  
Keyword(s):  
Optical Solitons ◽  
Equation Method ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Dwdm System ◽  
Extended Trial

Optical solitons for paraxial wave equation in Kerr media

2019 ◽  
Vol 33 (03) ◽  
pp. 1950020 ◽  
Author(s):  
Kashif Ali ◽  
Syed Tahir Raza Rizvi ◽  
Badar Nawaz ◽  
Muhammad Younis
Keyword(s):  
Wave Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Equation Method ◽  
Kerr Media ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Paraxial Wave Equation ◽  
Extended Trial

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.

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

Optik ◽  
2018 ◽  
Vol 158 ◽  
pp. 747-752 ◽  
Author(s):  
Anjan Biswas ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu ◽  
Fayequa B. Majid ◽  
Houria Triki ◽  
...  
Keyword(s):  
Optical Soliton ◽  
Equation Method ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Soliton Perturbation ◽  
Extended Trial
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