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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 (Izmir 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 solutions of a fractional-type differential-difference equation related to discrete MKdV equation Aslan, İsmail (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 ...
Aslan, İsmail (Indian Academy of Sciences, 2011-04)This paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical ...