Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
Browse
3 results
Search Results
Article Citation - WoS: 11Citation - Scopus: 12Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types(IOP Publishing Ltd., 2016) Aslan, İsmailDifferential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations, the majority of the results deal with polynomial types. Limited research has been reported regarding such equations of rational type. In this paper we present an adaptation of the (G′/G)-expansion method to solve nonlinear rational differential-difference equations. The procedure is demonstrated using two distinct equations. Our approach allows one to construct three types of exact traveling wave solutions (hyperbolic, trigonometric, and rational) by means of the simplified form of the auxiliary equation method with reduced parameters. Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.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.