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.Schrodinger equation

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 40
    Citation - Scopus: 40
    The Initial-Boundary Value Problem for the Biharmonic Schrödinger Equation on the Half-Line
    (American Institute of Mathematical Sciences, 2019) Özsarı, Türker; Yolcu, Nermin; Özsarı, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schrodinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for the solution of the linear nonhomogenenous problem by using the Fokas method (also known as the unified transform method). We use this representation formula to prove space and time estimates on the solutions of the linear model in fractional Sobolev spaces by using Fourier analysis. Secondly, we consider the nonlinear model with a power type nonlinearity and prove the local wellposedness by means of a classical contraction argument. We obtain Strichartz estimates to treat the low regularity case by using the oscillatory integral theory directly on the representation formula provided by the Fokas method. Global wellposedness of the defocusing model is established up to cubic nonlinearities by using the multiplier technique and proving hidden trace regularities.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    The Propagators for Δ and Δ′ Potentials With Time-Dependent Strengths
    (Frontiers Media S.A., 2020) Erman, Fatih; Erman, Fatih; Gadella, Manuel; Uncu, Haydar; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We study the time-dependent Schrodinger equation with finite number of Dirac delta and delta ' potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrodinger equation for delta ' potential with particular forms of the strengths.
  • 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.