Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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

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Author: search.filters.author.Pashaev, OktaySubject: search.filters.subject.Nonlinear Schrödinger equation

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  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Integrable Hierarchies and Information Measures
    (IOP Publishing Ltd., 2008) Parwani, Rajesh R.; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimensional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrödinger (NLS) equation. Depending on the choice of the enthalpy function, one obtains the cubic NLS or other modified NLS equations that have applications in various fields. Next, by considering the integrable hierarchy associated with the NLS model, we propose higher order information measures which include the Fisher measure as their first member. The lowest members of the hierarchy are shown to be included in the expansion of a regularized Kullback-Leibler measure while, on the other hand, a suitable combination of the NLS hierarchy leads to a Wootters type measure related to a NLS equation with a relativistic dispersion relation. Finally, through our approach, we are led to construct integrable relativistic NLS equations.
  • Article
    Citation - WoS: 91
    Citation - Scopus: 91
    Resonance Solitons as Black Holes in Madelung Fluid
    (World Scientific Publishing Co. Pte Ltd, 2002) Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    Envelope solitons of the Nonlinear Schrödinger equation (NLS) under quantum potential's influence are studied. Corresponding problem is found to be integrable for an arbitrary strength, s ≠ 1, of the quantum potential. For s < 1, the model is equivalent to the usual NLS with rescaled coupling constant, while for s > 1, to the reaction-diffusion system. The last one is related to the anti-de Sitter (AdS) space valued Heisenberg model, realizing a particular gauge fixing condition of the (1 + 1)-dimensional Jackiw-Teitelboim gravity. For this gravity model, by the Madelung fluid representation we derive the acoustic form of the space-time metric. The space-time points, where dispersion changes the sign, correspond to the event horizon, while the soliton solution to the AdS black hole. Moving with the above bounded velocity, it describes evolution on the one sheet hyperboloid with nontrivial winding number, and creates under collision, the resonance states which we study by the Hirota bilinear method.