Mathematics / Matematik

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

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  • Article
    Comment On: the (g'/g)-expansion Method for the Nonlinear Lattice Equations [commun Nonlinear Sci Numer Simulat 17 (2012) 3490-3498]
    (Elsevier, 2012) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We show that two of the nonlinear lattice equations studied by Ayhan & Bekir [Commun Nonlinear Sci Numer Simulat 17 (2012) 3490-3498] have already been investigated by Aslan [Commun Nonlinear Sci Numer Simulat 15 (2010) 1967-1973] using an improved version of the same method. The solutions obtained by the latter one include the solutions obtained by the former one. © 2012 Elsevier B.V.
  • Article
    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; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.