Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 25Citation - Scopus: 25Exact and Explicit Solutions To the Discrete Nonlinear Schrödinger Equation With a Saturable Nonlinearity(Elsevier Ltd., 2011) Aslan, İsmailWe 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 constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before. © 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 77Citation - Scopus: 110Analytic Study on Two Nonlinear Evolution Equations by Using the (g'/g)-expansion Method(Elsevier Ltd., 2009) Aslan, İsmail; Öziş, TurgutThe validity and reliability of the so-called (G′/G)-expansion method is tested by applying it to two nonlinear evolutionary equations. Solutions in more general forms are obtained. When the parameters are taken as special values, it is observed that the previously known solutions can be recovered. New rational function solutions are also presented. Being concise and less restrictive, the method can be applied to many nonlinear partial differential equations.Article Citation - WoS: 50Citation - Scopus: 56On the Validity and Reliability of the (g'/g)-expansion Method by Using Higher-Order Nonlinear Equations(Elsevier Ltd., 2009) Aslan, İsmail; Öziş, TurgutIn this study, we demonstrate the validity and reliability of the so-called (G′/G)-expansion method via symbolic computation. For illustrative examples, we choose the sixth-order Boussinesq equation and the ninth-order Korteweg-de-Vries equation. As a result, the power of the employed method is confirmed.Article Citation - WoS: 27Citation - Scopus: 28A Note on the (g'/g)-expansion Method Again(Elsevier Ltd., 2010) Aslan, İsmailWe report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved.Article Citation - WoS: 41Citation - Scopus: 56Exact and Explicit Solutions To Some Nonlinear Evolution Equations by Utilizing the (g'/g)-expansion Method(Elsevier Ltd., 2009) Aslan, İsmailIn 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 method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.Article Citation - WoS: 30Citation - Scopus: 36Discrete Exact Solutions To Some Nonlinear Differential-Difference Equations Via the (g'/g)-expansion Method(Elsevier Ltd., 2009) Aslan, İsmailWe 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.