Mathematics / Matematik

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

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Author: search.filters.author.Pashaev, OktaySubject: search.filters.subject.Schrodinger equation

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  • Article
    Relativistic Dissipatons in Integrable Nonlinear Majorana Type Spinor Model
    (Yunnan University, 2022) Pashaev, Oktay; Pashaev, Oktay; Lee, J. H.; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    By method of moving frame, the relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge equivalence of this model with Papanicolau spin model on one sheet hyperboloid is established. In terms of the so called double numbers, the model is represented also as hyperbolic complex relativistic model, in the form similar to the massive Thirring model. By using Hirota's bilinear method, the one dissipaton solution of this model is constructed. We calculate first integrals of motion for this dissipaton and show that it represents a relativistic particle with highly nonlinear mass. Analyzing resonance conditions for scattering of two relativistic dissipatons, we find a solution describing resonant property of the dissipatons.
  • 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.