Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2372
Title: Integrable hierarchies and information measures
Authors: Parwani, Rajesh R.
Pashaev, Oktay
Keywords: Information theory
Schrödinger equation
Nonlinear Schrödinger equation
Hydrodynamics
Issue Date: Jun-2008
Publisher: IOP Publishing Ltd.
Source: Parwani, R. R., and Pashaev, O. (2008). Integrable hierarchies and information measures. Journal of Physics A: Mathematical and Theoretical, 41(23), doi:10.1088/1751-8113/41/23/235207
Abstract: 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.
URI: http://doi.org/10.1088/1751-8113/41/23/235207
http://hdl.handle.net/11147/2372
ISSN: 1751-8113
1751-8113
1751-8121
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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