Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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

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Institution Author: search.filters.institutionAuthor.Pashaev, OktaySubject: search.filters.subject.Hydrodynamics

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Chiral Resonant Solitons in Chern-Simons Theory and Broer-Kaup Type New Hydrodynamic Systems
    (Elsevier Ltd., 2012) Lee, Jyh Hao; Pashaev, Oktay
    New Broer-Kaup type systems of hydrodynamic equations are derived from the derivative reaction-diffusion systems arising in SL(2, R) Kaup-Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of chiral solitons in quantum potential as a dimensional reduction of 2 + 1 dimensional Chern-Simons theory for anyons is shown. By the Hirota bilinear method, soliton solutions are constructed and the resonant character of soliton interaction is found.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Madelung Representation of Damped Parametric Quantum Oscillator and Exactly Solvable Schrödinger-Burgers Equations
    (American Institute of Physics, 2010) Atılgan Büyükaşık, Şirin; Pashaev, Oktay
    We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schrödinger equation with time-dependent parameters. It allows us to find exact solutions of the nonlinear Madelung system in terms of solutions of the Schrödinger equation and the corresponding classical linear ordinary differential equation with variable frequency and damping. For the complex velocity field, the Madelung system takes the form of a nonlinear complex Schrödinger-Burgers equation, for which we obtain exact solutions using complex Cole-Hopf transformation. In particular, we give exact results for nonlinear Madelung systems related with Caldirola-Kanai-type dissipative harmonic oscillator. Collapse of the wave function in dissipative models and possible implications for the quantum cosmology are discussed. © 2010 American Institute of Physics.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Integrable Hierarchies and Information Measures
    (IOP Publishing Ltd., 2008) Parwani, Rajesh R.; Pashaev, Oktay
    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.