Some mathematical aspects of the correspondence between the generalized nonlinear Schroedinger equation and the generalized Korteweg-de Vries equation

Journal Article · Tue Nov 10 00:00:00 EST 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3266814· OSTI ID:21335676

Fedele, Renato ^[1]; De Nicola, Sergio ^[2]; Grecu, Dan; Visinescu, Anca ^[3]; Shukla, Padma K ^[4]

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1. Dipartimento di Scienze Fisiche, Universita Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, I-80126 Napoli (Italy)
2. Istituto di Cibernetica del C.N.R. 'Eduardo Caianiello', Viale Campi Flegrei, 34, I-80078 Pozzuoli (Italy)
3. Department of Theoretical Physics, 'Horia Hulubei' National Institute for Physics and Nuclear Engineering, Bucharest (Romania)
4. Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitet Bochum, D-44780 Bochum (Germany)

A review of the recent studies on the correspondence between a wide family of the generalized nonlinear Schroedinger equations and a wide family of the generalized Korteweg-de Vries equations is presented. It was constructed some years ago within the framework of a recently-developed approach based on the Madelung's fluid representation of the generalized nonlinear Schroedinger equation. The present analysis extends the former approach, developed for nonlinear Schroedinger equation with a nonlinear term proportional to a multiplicative operator, to the cases of derivative operators and the ones corresponding to cylindrical nonlinear Schroedinger equations.

• OSTI ID: 21335676
• Journal Information: AIP Conference Proceedings, Vol. 1188, Issue 1; Conference: 2009 ICTP summer college on plasma physics; International symposium on cutting edge plasma physics, Trieste (Italy), 10-28 Aug 2009; Other Information: DOI: 10.1063/1.3266814; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
CYLINDRICAL CONFIGURATION
FLUID MECHANICS
FLUIDS
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
SCHROEDINGER EQUATION