Now showing items 1-10 of 13
Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method
We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. ...
A note on the (G′/G)-expansion method again
We report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved.
Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G′/G)-expansion method
In this paper, we demonstrate the effectiveness of the so-called (G′/G)-expansion method by examining some nonlinear evolution equations with physical interest. Our work is motivated by the fact that the (G′/G)-expansion ...
The discrete (G′/G)-expansion method applied to the differential-difference Burgers equation and the relativistic Toda lattice system
We introduce the discrete (G′/G)-expansion method for solving nonlinear differential-difference equations (NDDEs). As illustrative examples, we consider the differential-difference Burgers equation and the relativistic ...
Analytic study on two nonlinear evolution equations by using the (G′/G)-expansion method
The validity and reliability of the so-called (G′/G)-expansion method is tested by applying it to two nonlinear evolutionary equations. Solutions in more general forms are obtained. When the parameters are taken as special ...
Symbolic computation and construction of new exact traveling wave solutions to Fitzhugh-Nagumo and Klein-Gordon equations
(Verlag der Zeitschrift für Naturforschung, 2009)
With the aid of the symbolic computation system Mathematica, many exact solutions for the Fitzhugh-Nagumo equation and the Klein-Gordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, ...
On the validity and reliability of the (G′/G)-expansion method by using higher-order nonlinear equations
In this study, we demonstrate the validity and reliability of the so-called (G′/G)-expansion method via symbolic computation. For illustrative examples, we choose the sixth-order Boussinesq equation and the ninth-order ...
Analytic investigation of a reaction-Diffusion brusselator model with the time-space fractional derivative
(De Gruyter, 2014-04)
It is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we ...
An analytic approach to a class of fractional differential-difference equations of rational type via symbolic computation
Fractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differential-difference equations in the sense of Jumarie's modified ...
Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform
Dynamical behavior of many nonlinear systems can be described by fractional-order equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact ...