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. Discrete soliton and periodic wave solutions with more arbitrary parameters, as well as discrete rational wave solutions, are revealed. It seems that the utilized method can provide highly accurate discrete exact solutions to NDDEs arising in applied mathematical and physical sciences.
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Korkut Uysal, Sıla Övgü (İzmir Institute of Technology, 2015-06)This thesis proposes two different numerical methods for solving nonlinear oscillation problems which appear in engineering and physics. Thus, the study is conducted in two parts. The first part introduces and analyzes ...
Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G′/G)-expansion method Aslan, İsmail (Elsevier, 2009-09)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 Aslan, İsmail (Elsevier, 2013-11)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 ...