Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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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: 9Citation - Scopus: 8Similarity Solutions To Burgers' Equation in Terms of Special Functions of Mathematical Physics(Jagellonian University, 2017) Öziş, Turgut; Aslan, İsmailIn this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is reduced to ordinary differential equations whose general solutions are written in terms of the error function, Kummer's confluent hypergeometric function Φ(a; b; x) and Bessel functions Jp, showing the strong connection between the best mathematical modelling equations and the special functions of mathematical physics.Article Citation - WoS: 10Citation - Scopus: 11Some Exact and Explicit Solutions for Nonlinear Schrödinger Equations(Polish Academy of Sciences, 2013) Aslan, İsmailNonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödinger-type equations in terms of traveling wave solutions. Through the established first integrals, exact traveling wave solutions are obtained under some parameter conditions.Article Citation - WoS: 17Citation - Scopus: 25The First Integral Method for Constructing Exact and Explicit Solutions To Nonlinear Evolution Equations(John Wiley and Sons Inc., 2012) Aslan, İsmailProblems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some further results using the so-called first integral method. By means of the established first integrals, some exact traveling wave solutions are obtained in a concise manner.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: 16Citation - Scopus: 16Comment On: "application of Exp-Function Method for (3+1 )-Dimensional Nonlinear Evolution Equations" [comput. Math. Appl. 56 (2008) 14511456](Elsevier Ltd., 2011) Aslan, İsmailWe show that Boz and Bekir [A. Boz, A. Bekir, Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations, Comput. Math. Appl. 56 (2008) 14511456] obtained some incorrect solutions for the equations studied by means of the Exp-function method. We verify our assertion by direct substitution and pole order analysis. In addition, we provide the correct results using the same approach.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: 34Citation - Scopus: 34Exact and Explicit Solutions To Nonlinear Evolution Equations Using the Division Theorem(Elsevier Ltd., 2011) Aslan, İsmailIn this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a parameter condition. Our method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are derived in a concise manner.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.