Mathematics / Matematik

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

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Now showing 1 - 4 of 4
  • Article
    Traveling Waves of Ddes With Rational Nonlinearity
    (Walter de Gruyter GmbH, 2016) Aslan, İsmail
    It has been found that the dynamical behavior of many complex physical systems can be properly described by nonlinear DDEs. However, in the related literature, research focusing on such equations with rational nonlinearity is rare. Hence, the present study makes an attempt to fill the existing gap. To this end, we consider two distinct DDEs with rational nonlinearity. We observed that the model equations assume three kinds of traveling wave solutions; hyperbolic, trigonometric and rational including kink-type solitary waves and singular periodic solutions. Our discussion is based on the auxiliary equation method.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 16
    Analytic Investigation of a Reaction-Diffusion Brusselator Model With the Time-Space Fractional Derivative
    (Walter de Gruyter GmbH, 2014) Aslan, İsmail
    It is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we propose a reaction-diffusion Brusselator model from the viewpoint of the Jumarie's modified Riemann-Liouville fractional derivative. Based on the (G'/G)-expansion method, various kinds of exact solutions are obtained. Our results could be used as a starting point for numerical procedures as well.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 9
    Multi-Wave and Rational Solutions for Nonlinear Evolution Equations
    (Walter de Gruyter GmbH, 2010) Aslan, İsmail
    Nonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.
  • Article
    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.