Now showing items 1-10 of 48
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 ...
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 ...
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 ...
Construction of exact solutions for fractional-type difference-differential equations via symbolic computation
This paper deals with fractional-type difference-differential equations by means of the extended simplest equation method. First, an equation related to the discrete KdV equation is considered. Second, a system related to ...
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 ...
Rational and multi-wave solutions to some nonlinear physical models
(Romanian Academy, 2013)
The Exp-function method is shown to be an effective tool to explicitly construct rational and multi-wave solutions of completely integral nonlinear evolution equations. The procedure does not require the bilinear representation ...
Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the (3 + 1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and ...