A review of the recent studies on the correspondence between a wide family of the generalized nonlinear Schrodinger 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 Schrodinger equation. The present analysis extends the former approach, developed for nonlinear Schrodinger equation with a nonlinear term proportional to a multiplicative operator, to the cases of derivative operators and the ones corresponding to cylindrical nonlinear Schrodinger equations.
Some mathematical aspects of the correspondence between the generalized nonlinear Schroedinger equation and the generalized Korteweg-de Vries equation / Fedele, Renato; S., de Nicola; D., Grecu; A., Visinescu; P. K., Shukla. - STAMPA. - AIP Conf. Proc. vol. 1188:(2009), pp. 365-379. (Intervento presentato al convegno 2009 ICTP Summer College on Plasma Physics and International Symposium on Cutting Edge Plasma Physics tenutosi a Trieste, Italy nel 10-28 August, 2009) [10.1063/1.3266814].
Some mathematical aspects of the correspondence between the generalized nonlinear Schroedinger equation and the generalized Korteweg-de Vries equation
FEDELE, RENATO;
2009
Abstract
A review of the recent studies on the correspondence between a wide family of the generalized nonlinear Schrodinger 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 Schrodinger equation. The present analysis extends the former approach, developed for nonlinear Schrodinger equation with a nonlinear term proportional to a multiplicative operator, to the cases of derivative operators and the ones corresponding to cylindrical nonlinear Schrodinger equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
