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Now showing 1 - 7 of 7

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: 1
Citation - Scopus: 2
Application of the Division Theorem To Nonlinear Physical Models for Constructing Traveling Waves
(Politechnica University of Bucharest, 2013) Aslan, İsmail
We extend the so-called first integral method, which is based on the division theorem, to the Sharma-Tasso-Olver equation and the (2+1)-dimensional modified Boussinesq equation. Our approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Traveling wave solutions are constructed through the established first integrals.
Citation - WoS: 10
Citation - Scopus: 11
Some Exact and Explicit Solutions for Nonlinear Schrödinger Equations
(Polish Academy of Sciences, 2013) Aslan, İsmail
Nonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödinger-type equations in terms of traveling wave solutions. Through the established first integrals, exact traveling wave solutions are obtained under some parameter conditions.
Citation - WoS: 13
Citation - Scopus: 14
Rational and Multi-Wave Solutions To Some Nonlinear Physical Models
(Editions de l'Academie Republique Populaire, 2013) Aslan, İsmail
The Exp-function method is shown to be an effective tool to explicitly construct rational and multi-wave solutions of completely integral nonlinear evolution equations. The procedure does not require the bilinear representation of the equation. The method is straightforward, concise, and its applications to other types of nonlinear evolution equations are promising.
Citation - WoS: 8
Citation - Scopus: 8
Some Exact and Explicit Solutions To a Two-Component, Discrete, Nonlinear Schrödinger Model
(National Research Council of Canada, 2011) Aslan, İsmail
Natural processes and phenomena often display discrete structure. The discrete nonlinear Schrödinger equations are used in both physics and biology to model periodic optical structures and energy transfer in proteins. In this study, we present a new application of the (G'/G)-expansion method to special, coupled, discrete, nonlinear Schrödinger-type equations. This application is shown to be an effective tool for constructing solitary and periodic wave profiles with arbitrary parameters. In addition, we provide rational solutions that have not been explicitly computed before.
Citation - WoS: 3
Citation - Scopus: 3
Rational and Multi-Wave Solutions To Nonlinear Evolution Equations by Means of the Exp-Function Method
(Politechnica University of Bucharest, 2012) Aslan, İsmail
In this paper, we present a new application of the Exp-function method to carry out the integration of nonlinear evolution equations in terms of multi-wave and rational solutions. To elucidate the solution procedure, we analytically investigate the Sharma-Tasso-Olver equation and the fifth-order Korteweg de Vries equation. Unlike Hirota's method, our procedure does not require the bilinear formalism of the equations studied.
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.

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