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Now showing 1 - 7 of 7

Citation - WoS: 32
Citation - Scopus: 37
Symbolic Computation and Construction of New Exact Traveling Wave Solutions To Fitzhugh-Nagumo and Klein-Gordon Equations
(Walter de Gruyter GmbH, 2009) Öziş, Turgut; Aslan, İsmail
With the aid of the symbolic computation system Mathematica, many exact solutions for the Fitzhugh-Nagumo equation and the Klein-Gordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, the so-called (G'/G)-expansion method, where the new and more general forms of solutions are also obtained. Periodic and solitary traveling wave solutions capable of moving in both directions are observed.
Citation - WoS: 77
Citation - Scopus: 110
Analytic Study on Two Nonlinear Evolution Equations by Using the (g'/g)-expansion Method
(Elsevier Ltd., 2009) Aslan, İsmail; Öziş, Turgut
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: 50
Citation - Scopus: 56
On the Validity and Reliability of the (g'/g)-expansion Method by Using Higher-Order Nonlinear Equations
(Elsevier Ltd., 2009) Aslan, İsmail; Öziş, Turgut
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: 41
Citation - Scopus: 56
Exact and Explicit Solutions To Some Nonlinear Evolution Equations by Utilizing the (g'/g)-expansion Method
(Elsevier Ltd., 2009) Aslan, İsmail
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: 1
Citation - Scopus: 1
The Extended Discrete (g'/g)-expansion Method and Its Application To the Relativistic Toda Lattice System
(American Institute of Physics, 2009) Aslan, İsmail
We propose the extended discrete (G′/G)-expansion method for directly solving nonlinear differentialdifference equations. For illustration, we choose the relativistic Toda lattice system. We derive further discrete hyperbolic and trigonometric function traveling wave solutions, as well as discrete rational function solutions.
Citation - WoS: 30
Citation - Scopus: 36
Discrete Exact Solutions To Some Nonlinear Differential-Difference Equations Via the (g'/g)-expansion Method
(Elsevier Ltd., 2009) Aslan, İsmail
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: 64
Citation - Scopus: 80
Exact and Explicit Solutions To the (3 + 1)-Dimensional Jimbo-Miwa Equation Via the Exp-Function Method
(Elsevier Ltd., 2008) Öziş, Turgut; Aslan, İsmail
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the (3 + 1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. Being less restrictive and concise, the method can be applied to many high-dimensional nonlinear evolution equations having wide applications in applied physical sciences. © 2008 Elsevier B.V. All rights reserved

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