Now showing items 1-10 of 43
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. ...
Traveling wave solutions for nonlinear differential-difference equations of rational types
(Institute of Physics Publishing, 2016-01-01)
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out ...
Multi-wave and rational solutions for nonlinear evolution equations
(De Gruyter, 2010-08)
Nonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.
Exact solutions for a local fractional DDE associated with a nonlinear transmission line
(Institute of Physics Publishing, 2016-09-01)
Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which ...
Some remarks on Exp-function method and its applications - A supplement
(IOP Publishing, 2013-11)
Recently, the authors of [Commun. Theor. Phys. 56 (2011) 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function ...
Exact and explicit solutions to nonlinear evolution equations using the division theorem
In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a ...
Remark on:"Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation" [Appl. Math. Comput. (2009) doi:10.1016/j.amc.2009.07.009]
By means of the Exp-function method, Inan and Ugurlu [Appl. Math. Comput. (2009) doi:10.1016/j.amc.2009.07.009] reported eight expressions for being solutions to the two equations studied. In fact, all of them can be easily ...
Constructing rational and multi-wave solutions to higher order NEEs via the Exp-function method
In this paper, we present an application of some known generalizations of the Exp-function method to the fifth-order Burgers and to the seventh-order Korteweg de Vries equations for the first time. The two examples show ...
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.