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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 the well-known self-dual network equations through a real discrete Miura transformation is analyzed. As a consequence, three types of exact solutions (with the aid of symbolic computation) emerged; hyperbolic, trigonometric and rational which have not been reported before. Our results could be used as a starting point for numerical procedures as well.
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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 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 ...
Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method Aslan, İsmail (Elsevier, 2009-12)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. ...