Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5233
Title: Exactly solvable Madelung fluid and complex Burgers equations: A quantum Sturm-Liouville connection
Authors: Atılgan Büyükaşık, Şirin
Pashaev, Oktay
Keywords: Time variable parameters
Burgers equation
Madelung fluid
Sturm-Liouville problems
Quantum hydrodynamics
Issue Date: Nov-2012
Publisher: Springer Verlag
Source: Atılgan Büyükaşık, Ş., and Pashaev, O. (2012). Exactly solvable Madelung fluid and complex Burgers equations: A quantum Sturm-Liouville connection. Journal of Mathematical Chemistry, 50(10), 2716-2745. doi:10.1007/s10910-012-0060-4
Abstract: Quantum Sturm-Liouville problems introduced in our paper (Büyükaşi{dotless}k et al. in J Math Phys 50:072102, 2009) provide a reach set of exactly solvable quantum damped parametric oscillator models. Based on these results, in the present paper we study a set of variable parametric nonlinear Madelung fluid models and corresponding complex Burgers equations, related to the classical orthogonal polynomials of Hermite, Laguerre and Jacobi types. We show that the nonlinear systems admit direct linearazation in the form of Schrödinger equation for a parametric harmonic oscillator, allowing us to solve exactly the initial value problems for these equations by the linear quantum Sturm-Liouville problem. For each type of equations, dynamics of the probability density and corresponding zeros, as well as the complex velocity field and related pole singularities are studied in details. © 2012 Springer Science+Business Media, LLC.
URI: http://doi.org/10.1007/s10910-012-0060-4
http://hdl.handle.net/11147/5233
ISSN: 0259-9791
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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