Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Now showing 1 - 15 of 15

Citation - WoS: 17
Citation - Scopus: 18
The Ablowitz-Ladik Lattice System by Means of the Extended (g' / G)-Expansion Method
(Elsevier Ltd., 2010-07) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We analyzed the Ablowitz-Ladik lattice system by using the extended (G′ / G)-expansion method. Further discrete soliton and periodic wave solutions with more arbitrary parameters are obtained. We observed that some previously known results can be recovered by assigning special values to the arbitrary parameters. © 2010 Elsevier Inc. All rights reserved.
Citation - WoS: 16
Citation - Scopus: 16
Analytic Investigation of the (2 + 1)-Dimensional Schwarzian Korteweg–de Vries Equation for Traveling Wave Solutions
(Elsevier Ltd., 2011-02-15) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
By 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.
Citation - WoS: 77
Citation - Scopus: 110
Analytic Study on Two Nonlinear Evolution Equations by Using the (g'/g)-expansion Method
(Elsevier Ltd., 2009-03) Aslan, İsmail; Öziş, Turgut; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The 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.
Citation - WoS: 29
Citation - Scopus: 48
Application of the G' / G-Expansion Method To Kawahara Type Equations Using Symbolic Computation
(Elsevier Ltd., 2010-06) Öziş, Turgut; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In 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.
Citation - WoS: 30
Citation - Scopus: 36
Discrete Exact Solutions To Some Nonlinear Differential-Difference Equations Via the (g'/g)-expansion Method
(Elsevier Ltd., 2009-12) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. Discrete soliton and periodic wave solutions with more arbitrary parameters, as well as discrete rational wave solutions, are revealed. It seems that the utilized method can provide highly accurate discrete exact solutions to NDDEs arising in applied mathematical and physical sciences.
Citation - WoS: 34
Citation - Scopus: 34
Exact and Explicit Solutions To Nonlinear Evolution Equations Using the Division Theorem
(Elsevier Ltd., 2011-06) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In 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.
Citation - WoS: 40
Citation - Scopus: 56
Exact and Explicit Solutions To Some Nonlinear Evolution Equations by Utilizing the (g'/g)-expansion Method
(Elsevier Ltd., 2009-09) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In 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.
Citation - WoS: 22
Citation - Scopus: 31
Generalized Solitary and Periodic Wave Solutions To a (2 + 1)-Dimensional Zakharov-Kuznetsov Equation
(Elsevier Ltd., 2010-10) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In 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.
Citation - WoS: 27
Citation - Scopus: 28
A Note on the (g'/g)-expansion Method Again
(Elsevier Ltd., 2010-09) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 4
On the Application of the Exp-Function Method To Nonlinear Differential-Difference Equations
(Elsevier Ltd., 2012-06) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
When applying the Exp-function method to nonlinear-differential difference equations, Bekir (2010) [1] reported incorrect results. © 2012 Elsevier Inc. All rights reserved.
Citation - WoS: 22
Citation - Scopus: 26
On the Application of the Exp-Function Method To the Kp Equation for N-Soliton Solutions
(Elsevier, 2012-11) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We 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.
Citation - WoS: 4
Citation - Scopus: 7
On the Numerical Solution of Korteweg-De Vries Equation by the Iterative Splitting Method
(Elsevier Ltd., 2011-10) Gücüyenen, Nurcan; Tanoğlu, Gamze; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In this paper, we apply the method of iterative operator splitting on the Korteweg-de Vries (KdV) equation. The method is based on first, splitting the complex problem into simpler sub-problems. Then each sub-equation is combined with iterative schemes and solved with suitable integrators. Von Neumann analysis is performed to achieve stability criteria for the proposed method applied to the KdV equation. The numerical results obtained by iterative splitting method for various initial conditions are compared with the exact solutions. It is seen that they are in a good agreement with each other. © 2011 Elsevier Inc. All rights reserved.
Citation - WoS: 50
Citation - Scopus: 56
On the Validity and Reliability of the (g'/g)-expansion Method by Using Higher-Order Nonlinear Equations
(Elsevier Ltd., 2009-05) Aslan, İsmail; Öziş, Turgut; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In 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.
Citation - WoS: 6
Citation - Scopus: 4
Remark 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., 2010-12) Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
By 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.
Citation - WoS: 15
Citation - Scopus: 14
Strang Splitting Method for Burgers-Huxley Equation
(Elsevier Ltd., 2016-03-05) Çiçek, Yeşim; Tanoğlu, Gamze; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We derive an analytical approach to the Strang splitting method for the Burgers-Huxley equation (BHE) ut+αuux-ε uXX=β(1-u)(u-γ)u. We proved that Srtang splitting method has a second order convergence in Hs(R), where Hs(R) is the Sobolev space and s is an arbitrary nonnegative integer. We numerically solve the BHE by Strang splitting method and compare the results with the reference solution.

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