Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 6Citation - Scopus: 4Remark On:"exp-Function Method for the Exact Solutions of Fifth Order Kdv Equation and Modified Burgers Equation" [appl. Math. Comput. (2009) Doi:10.1016/J.amc.2009.07.009](Elsevier Ltd., 2010) Aslan, İsmailBy means of the Exp-function method, Inan and Ugurlu [Appl. Math. Comput. (2009) doi:10.1016/j.amc.2009.07.009] reported eight expressions for being solutions to the two equations studied. In fact, all of them can be easily simplified to constants.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: 13Citation - Scopus: 14Rational and Multi-Wave Solutions To Some Nonlinear Physical Models(Editions de l'Academie Republique Populaire, 2013) Aslan, İsmailThe Exp-function method is shown to be an effective tool to explicitly construct rational and multi-wave solutions of completely integral nonlinear evolution equations. The procedure does not require the bilinear representation of the equation. The method is straightforward, concise, and its applications to other types of nonlinear evolution equations are promising.Article Citation - WoS: 22Citation - Scopus: 26On the Application of the Exp-Function Method To the Kp Equation for N-Soliton Solutions(Elsevier, 2012) Aslan, İsmailWe observe that the form of the Kadomstev-Petviashvili equation studied by Yu (2011) [S. Yu, N-soliton solutions of the KP equation by Exp-function method, Appl. Math. Comput. (2011) doi:10.1016/j.amc.2010.12.095] is incorrect. We claim that the N-soliton solutions obtained by means of the basic Exp-function method and some of its known generalizations do not satisfy the equation considered. We emphasize that Yu's results (except only one) cannot be solutions of the correct form of the Kadomstev-Petviashvili equation. In addition, we provide some correct results using the same approach.Article Citation - WoS: 17Citation - Scopus: 16Some Remarks on Exp-Function Method and Its Applications - a Supplement(IOP Publishing Ltd., 2013) Aslan, İsmailRecently, the authors of [Commun. Theor. Phys. 56 (2011) 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function method.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: 16Citation - Scopus: 15Constructing Rational and Multi-Wave Solutions To Higher Order Nees Via the Exp-Function Method(John Wiley and Sons Inc., 2011) Aslan, İsmailIn this paper, we present an application of some known generalizations of the Exp-function method to the fifth-order Burgers and to the seventh-order Korteweg de Vries equations for the first time. The two examples show that the Exp-function method can be an effective alternative tool for explicitly constructing rational and multi-wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered.Article Citation - WoS: 4Citation - Scopus: 4On the Application of the Exp-Function Method To Nonlinear Differential-Difference Equations(Elsevier Ltd., 2012) Aslan, İsmailWhen applying the Exp-function method to nonlinear-differential difference equations, Bekir (2010) [1] reported incorrect results. © 2012 Elsevier Inc. All rights reserved.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.