Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Traveling Waves of Ddes With Rational Nonlinearity(Walter de Gruyter GmbH, 2016) Aslan, İsmailIt has been found that the dynamical behavior of many complex physical systems can be properly described by nonlinear DDEs. However, in the related literature, research focusing on such equations with rational nonlinearity is rare. Hence, the present study makes an attempt to fill the existing gap. To this end, we consider two distinct DDEs with rational nonlinearity. We observed that the model equations assume three kinds of traveling wave solutions; hyperbolic, trigonometric and rational including kink-type solitary waves and singular periodic solutions. Our discussion is based on the auxiliary equation method.Article Citation - WoS: 14Citation - Scopus: 16Analytic Investigation of a Reaction-Diffusion Brusselator Model With the Time-Space Fractional Derivative(Walter de Gruyter GmbH, 2014) Aslan, İsmailIt is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we propose a reaction-diffusion Brusselator model from the viewpoint of the Jumarie's modified Riemann-Liouville fractional derivative. Based on the (G'/G)-expansion method, various kinds of exact solutions are obtained. Our results could be used as a starting point for numerical procedures as well.Article Citation - WoS: 9Citation - Scopus: 9Multi-Wave and Rational Solutions for Nonlinear Evolution Equations(Walter de Gruyter GmbH, 2010) Aslan, İsmailNonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.Article Citation - WoS: 6Citation - Scopus: 6Construction of Exact Solutions for Fractional-Type Difference-Differential Equations Via Symbolic Computation(Elsevier Ltd., 2013) Aslan, İsmailThis 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.Article Citation - WoS: 3Citation - Scopus: 2Application of the Exp-Function Method To the (2+1)-Dimensional Boiti-Leon Equation Using Symbolic Computation(Taylor and Francis Ltd., 2011) Aslan, İsmailLocate full-text(opens in a new window)|Full Text(opens in a new window)|View at Publisher| Export | Download | Add to List | More... International Journal of Computer Mathematics Volume 88, Issue 4, March 2011, Pages 747-761 Application of the Exp-function method to the (2+1)-dimensional Boiti-Leon-Pempinelli equation using symbolic computation (Article) Aslan, I. Department of Mathematics, Izmir Institute of Technology, Urla, Izmir 35430, Turkey View references (47) Abstract This paper deals with the so-called Exp-function method for studying a particular nonlinear partial differential equation (PDE): the (2+1)-dimensional Boiti-Leon-Pempinelli equation. The method is constructive and can be carried out in a computer with the aid of a computer algebra system. The obtained generalized solitary wave solutions contain more arbitrary parameters compared with the earlier works, and thus, they are wider. This means that our method is effective and powerful for constructing exact and explicit analytic solutions to nonlinear PDEs.Article Citation - WoS: 23Citation - Scopus: 26Travelling Wave Solutions To Nonlinear Physical Models by Means of the First Integral Method(Springer Verlag, 2011) Aslan, İsmailThis paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established first integrals, exact solutions are successfully constructed for the equations considered. © Indian Academy of Sciences.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: 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.Article Citation - WoS: 64Citation - Scopus: 80Exact and Explicit Solutions To the (3 + 1)-Dimensional Jimbo-Miwa Equation Via the Exp-Function Method(Elsevier Ltd., 2008) Öziş, Turgut; Aslan, İsmailIn this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the (3 + 1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. Being less restrictive and concise, the method can be applied to many high-dimensional nonlinear evolution equations having wide applications in applied physical sciences. © 2008 Elsevier B.V. All rights reserved