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: 32Citation - Scopus: 37Symbolic Computation and Construction of New Exact Traveling Wave Solutions To Fitzhugh-Nagumo and Klein-Gordon Equations(Walter de Gruyter GmbH, 2009) Öziş, Turgut; Aslan, İsmailWith the aid of the symbolic computation system Mathematica, many exact solutions for the Fitzhugh-Nagumo equation and the Klein-Gordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, the so-called (G'/G)-expansion method, where the new and more general forms of solutions are also obtained. Periodic and solitary traveling wave solutions capable of moving in both directions are observed.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: 32Citation - Scopus: 49Application of the G' / G-Expansion Method To Kawahara Type Equations Using Symbolic Computation(Elsevier Ltd., 2010) Öziş, Turgut; Aslan, İsmailIn this paper, Kawahara type equations are selected to illustrate the effectiveness and simplicity of the G′ / G-expansion method. With the aid of a symbolic computation system, three types of more general traveling wave solutions (including hyperbolic functions, trigonometric functions and rational functions) with free parameters are constructed. Solutions concerning solitary and periodic waves are also given by setting the two arbitrary parameters, involved in the traveling waves, as special values. © 2010 Elsevier Inc. All rights reserved.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.