Multiscale expansions for a generalized cylindrical nonlinear Schrodinger equation

Considering a (3 + 1)-dimensional generalized nonlinear Schrodinger equatio n, we use the reductive multiscale expansion method to derive new evolution equations for small-amplitude solitary waves on a finite background. These equations are a combination of the so-called Johnson's and a CI equation f or the spatial solitons, and a CII equation for the temporal solitons. It i s shown that the simplest one-dimensional soliton solutions to these two eq uations are either dark or anti-dark, depending on the type of the nonlinea rity and a value of the background amplitude. It is also demonstrated that one can easily switch a dark soliton into an anti-dark one, increasing the background intensity. (C) 1999 Elsevier Science B.V. All rights reserved.