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Now showing 1 - 6 of 6

Citation - WoS: 9
Citation - Scopus: 8
Similarity Solutions To Burgers' Equation in Terms of Special Functions of Mathematical Physics
(Jagellonian University, 2017) Öziş, Turgut; Aslan, İsmail
In this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is reduced to ordinary differential equations whose general solutions are written in terms of the error function, Kummer's confluent hypergeometric function Φ(a; b; x) and Bessel functions Jp, showing the strong connection between the best mathematical modelling equations and the special functions of mathematical physics.
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: 32
Citation - Scopus: 49
Application of the G' / G-Expansion Method To Kawahara Type Equations Using Symbolic Computation
(Elsevier Ltd., 2010) Öziş, Turgut; Aslan, İsmail
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: 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: 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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