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: 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: 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: 9Citation - Scopus: 10Application of the Exp-Function Method To Nonlinear Lattice Differential Equations for Multi-Wave and Rational Solutions(John Wiley and Sons Inc., 2011) Aslan, İsmailIn this paper, we extend the basic Exp-function method to nonlinear lattice differential equations for constructing multi-wave and rational solutions for the first time. We consider a differential-difference analogue of the Korteweg-de Vries equation to elucidate the solution procedure. Our approach is direct and unifying in the sense that the bilinear formalism of the equation studied becomes redundant.Article Citation - WoS: 16Citation - Scopus: 16Analytic Investigation of the (2 + 1)-Dimensional Schwarzian Korteweg–de Vries Equation for Traveling Wave Solutions(Elsevier Ltd., 2011) Aslan, İsmailBy means of the two distinct methods, the Exp-function method and the extended (G0/G)-expansion method, we successfully performed an analytic study on the (2 + 1)-dimensional Schwarzian Korteweg–de Vries equation. We exhibited its further closed form traveling wave solutions which reduce to solitary and periodic waves. New rational solutions are also revealed.Article Citation - WoS: 21Citation - Scopus: 22The Exp-Function Approach To the Schwarzian Korteweg-De Vries Equation(Elsevier Ltd., 2010) Aslan, İsmailBy means of the Exp-function method and its generalization, we report further exact traveling wave solutions, in a concise form, to the Schwarzian Korteweg-de Vries equation which admits physical significance in applications. Not only solitary and periodic waves but also rational solutions are observed. © 2010 Elsevier Ltd. All rights reserved.Article Citation - WoS: 22Citation - Scopus: 31Generalized Solitary and Periodic Wave Solutions To a (2 + 1)-Dimensional Zakharov-Kuznetsov Equation(Elsevier Ltd., 2010) Aslan, İsmailIn this paper, the Exp-function method is employed to the Zakharov-Kuznetsov equation as a (2 + 1)-dimensional model for nonlinear Rossby waves. The observation of solitary wave solutions and periodic wave solutions constructed from the exponential function solutions reveal that our approach is very effective and convenient. The obtained results may be useful for better understanding the properties of two-dimensional coherent structures such as atmospheric blocking events. © 2009 Elsevier Inc. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 10Comment On: "new Exact Solutions for the Kawahara Equation Using Exp-Function Method" [j. Comput. Appl. Math. 233 (2009) 97102](Elsevier Ltd., 2010) Aslan, İsmailAssas [Laila M.B. Assas, New exact solutions for the Kawahara equation using Exp-function method, J. Comput. Appl. Math. 233 (2009) 97102] found some supposedly new exact solutions to the Kawahara equation by means of the Exp-function method. Unfortunately, they are incorrect. We emphasize that the article contains erroneous formulas and resulting relations. In fact, no numerical method was used. © 2010 Elsevier B.V. All rights reserved.