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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
(Elsevier, 2011-06)
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]
(Elsevier, 2010-12)
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 ...
Comment on: "New exact solutions for the Kawahara equation using Exp-function method" [J. Comput. Appl. Math. 233 (2009) 97102]
(Elsevier, 2010-10)
Assas [Laila M.B. Assas, New exact solutions for the Kawahara equation using Exp-function method, J. Comput. Appl. Math. 233 (2009) 97102] found some supposedly new exact solutions to the Kawahara equation by means of the ...
Constructing rational and multi-wave solutions to higher order NEEs via the Exp-function method
(Wiley, 2011-05)
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
(Elsevier, 2011-11-14)
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
(Elsevier, 2010-09)
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 solutions of a fractional-type differential-difference equation related to discrete MKdV equation
(IOP Publishing, 2014-05)
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete ...