Abundant travelling wave solutions for nonlinear Kawahara partial differential equation using extended trial equation method

2018 ◽  
Vol 96 (7) ◽  
pp. 1357-1376 ◽  
Author(s):  
Khaled A. Gepreel ◽  
Taher A. Nofal ◽  
Amera A. Al-Asmari
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Travelling Wave ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Extended Trial

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.

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.

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

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

scholarly journals Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Octavio Cornejo-Pérez ◽  
Haret Rosu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Second Order Differential Equation ◽  
Wave Solutions ◽  
Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

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