Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Department: search.filters.department.İzmir Institute of Technology. MathematicsSubject: search.filters.subject.Periodic structures

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  • Conference Object
    Citation - WoS: 8
    Citation - Scopus: 11
    Two-Circles Theorem, Q-Periodic Functions and Entangled Qubit States
    (IOP Publishing Ltd., 2014) Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    For arbitrary hydrodynamic flow in circular annulus we introduce the two circle theorem, allowing us to construct the flow from a given one in infinite plane. Our construction is based on q-periodic analytic functions for complex potential, leading to fixed scale-invariant complex velocity, where q is determined by geometry of the region. Self-similar fractal structure of the flow with q-periodic modulation as solution of q-difference equation is studied. For one point vortex problem in circular annulus by fixing singular points we find solution in terms of q-elementary functions. Considering image points in complex plane as a phase space for qubit coherent states we construct Fibonacci and Lucas type entangled N-qubit states. Complex Fibonacci curve related to this construction shows reach set of geometric patterns.
  • 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.