Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
Browse
9 results
Search Results
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: 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: 6Citation - Scopus: 6Some Exact Solutions for Toda Type Lattice Differential Equations Using the Improved (g'/g)-expansion Method(John Wiley and Sons Inc., 2012) Aslan, İsmailNonlinear lattice differential equations (also known as differential-difference equations) appear in many applications. They can be thought of as hybrid systems for the inclusion of both discrete and continuous variables. On the basis of an improved version of the basic (G′/G)- expansion method, we focus our attention towards some Toda type lattice differential systems for constructing further exact traveling wave solutions. Our method provides not only solitary and periodic wave profiles but also rational solutions with more arbitrary parameters. © 2012 John Wiley & Sons, Ltd.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.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: 32Citation - Scopus: 49Application of the G' / G-Expansion Method To Kawahara Type Equations Using Symbolic Computation(Elsevier Ltd., 2010) Öziş, Turgut; Aslan, İsmailIn this paper, Kawahara type equations are selected to illustrate the effectiveness and simplicity of the G′ / G-expansion method. With the aid of a symbolic computation system, three types of more general traveling wave solutions (including hyperbolic functions, trigonometric functions and rational functions) with free parameters are constructed. Solutions concerning solitary and periodic waves are also given by setting the two arbitrary parameters, involved in the traveling waves, as special values. © 2010 Elsevier Inc. All rights reserved.Article Citation - WoS: 50Citation - Scopus: 56On the Validity and Reliability of the (g'/g)-expansion Method by Using Higher-Order Nonlinear Equations(Elsevier Ltd., 2009) Aslan, İsmail; Öziş, TurgutIn this study, we demonstrate the validity and reliability of the so-called (G′/G)-expansion method via symbolic computation. For illustrative examples, we choose the sixth-order Boussinesq equation and the ninth-order Korteweg-de-Vries equation. As a result, the power of the employed method is confirmed.Article Citation - WoS: 41Citation - Scopus: 56Exact and Explicit Solutions To Some Nonlinear Evolution Equations by Utilizing the (g'/g)-expansion Method(Elsevier Ltd., 2009) Aslan, İsmailIn this paper, we demonstrate the effectiveness of the so-called (G′/G)-expansion method by examining some nonlinear evolution equations with physical interest. Our work is motivated by the fact that the (G′/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.