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On the mapping connecting the cylindrical nonlinear von Neumann equation with the standard von Neumann equation

Published online by Cambridge University Press:  25 January 2010

RENATO FEDELE ,
SERGIO DE NICOLA ,
DUSAN JOVANOVIĆ ,
DAN GRECU  and
ANCA VISINESCU
RENATO FEDELE
Affiliation:
Dipartimento di Scienze Fisiche, Università Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, via Cintia, I-80126 Napoli, Italy, EU (renato.fedele@na.infn.it)
SERGIO DE NICOLA
Affiliation:
Dipartimento di Scienze Fisiche, Università Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, via Cintia, I-80126 Napoli, Italy, EU (renato.fedele@na.infn.it) Istituto di Cibernetica “Eduardo Caianiello” del CNR Comprensorio “A. Olivetti” Fabbr. 70, Via Campi Flegrei, 34, I-80078 Pozzuoli (NA), Italy, EU
DUSAN JOVANOVIĆ
Affiliation:
Institute of Physics, P. O. Box 57, 11001 Belgrade, Serbia
DAN GRECU
Affiliation:
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering “Horia Hulubei”, Atomistilor 407, Bucharest-Magurele, RO-077125, Romania
ANCA VISINESCU
Affiliation:
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering “Horia Hulubei”, Atomistilor 407, Bucharest-Magurele, RO-077125, Romania
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Abstract

The Wigner transformation is used to define the quasidistribution (Wigner function) associated with the wave function of the cylindrical nonlinear Schrödinger equation (CNLSE) in a way similar to that of the standard nonlinear Schrödinger equation (NLSE). The phase-space equation, governing the evolution of such quasidistribution, is a sort of nonlinear von Neumann equation (NLvNE), called here the ‘cylindrical nonlinear von Neumann equation’ (CNLvNE). Furthermore, the phase-space transformations, connecting the Wigner function and the NLvNE with the ‘cylindrical Wigner function’ and the CNLvNE, are found by extending the configuration space transformations that connect the NLSE and the CNLSE. Some examples of phase-space soliton solutions are given analytically and evaluated numerically.

Type
Papers
Information
Journal of Plasma Physics , Volume 76 , Special Issue 3-4: In Honor of Professor Padma Kant Shukla on the Occasion of His 60th Birthday , August 2010 , pp. 645 - 653
Copyright
Copyright © Cambridge University Press 2010

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