Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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

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Publisher: search.filters.publisher.Elsevier Ltd.Subject: search.filters.subject.Crystal lattices

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 17
    Citation - Scopus: 18
    The Ablowitz-Ladik Lattice System by Means of the Extended (g' / G)-Expansion Method
    (Elsevier Ltd., 2010) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We analyzed the Ablowitz-Ladik lattice system by using the extended (G′ / G)-expansion method. Further discrete soliton and periodic wave solutions with more arbitrary parameters are obtained. We observed that some previously known results can be recovered by assigning special values to the arbitrary parameters. © 2010 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 22
    A Discrete Generalization of the Extended Simplest Equation Method
    (Elsevier Ltd., 2010) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We modified the so-called extended simplest equation method to obtain discrete traveling wave solutions for nonlinear differential-difference equations. The Wadati lattice equation is chosen to illustrate the method in detail. Further discrete soliton/periodic solutions with more arbitrary parameters, as well as discrete rational solutions, are revealed. We note that using our approach one can also find in principal highly accurate exact discrete solutions for other lattice equations arising in the applied sciences. © 2009 Elsevier B.V. All rights reserved.
  • Article
    Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model
    (Elsevier Ltd., 2008) Gürkan, Zeynep Nilhan; Pashaev, Oktay; Pashaev, Oktay; Gürkan, Zeynep Nilhan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    The problem of magnetic vortex dynamics in an anisotropic spin liquid model is considered. For incompressible flow the model admits reduction to saturating Bogomolny inequality analytic projections of spin variables, subject the linear holomorphic Schrödinger equation. It allows us to construct N vortex configurations in terms of the complex Hermite polynomials. Using complex Galilean boost transformations, the interaction of the vortices and the vortex chain lattices (vortex crystals) is studied. By the complexified Cole-Hopf transformation, integrable N vortex dynamics is described by the holomorphic Burgers equation. Mapping of the point vortex problem to N-particle problem, the complexified Calogero-Moser system, showing its integrability and the Hamiltonian structure, is given. © 2006 Elsevier Ltd. All rights reserved.