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. ...
Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity
We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G′/G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are ...
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.
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 ...
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 ...
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 ...
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 ...
Symbolic computation of exact solutions for fractional differential-difference equation models
(Vilnius University Institute of Mathematics and Informatics, 2014-11)
The aim of the present study is to extend the (G′=G)-expansion method to fractional differential-difference equations of rational type. Particular time-fractional models are considered to show the strength of the method. ...