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: 27Some Remarks on Exp-Function Method and Its Applications(IOP Publishing Ltd., 2011) Aslan, İsmail; Marinakis, VangelisRecently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.Conference Object Damped Parametric Oscillator and Exactly Solvable Complex Burgers Equations(IOP Publishing Ltd., 2012) Atılgan Büyükaşık, Şirin; Pashaev, OktayWe obtain exact solutions of a parametric Madelung fluid model with dissipation which is linearazible in the form of Schrödinger equation with time variable coefficients. The corresponding complex Burgers equation is solved by a generalized Cole-Hopf transformation and the dynamics of the pole singularities is described explicitly. In particular, we give exact solutions for variable parametric Madelung fluid and complex Burgers equations related with the Sturm-Liouville problems for the classical Hermite, Laguerre and Legendre type orthogonal polynomials.Article Citation - WoS: 26Citation - Scopus: 27Analytic Solutions To Nonlinear Differential-Difference Equations by Means of the Extended (g'/g)-expansion Method(IOP Publishing Ltd., 2010) Aslan, İsmailIn this paper, a discrete extension of the (G′/G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schrödinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising. © 2010 IOP Publishing Ltd.