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;
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.
9780735407541
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/365516
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