D ANDERSON, M LISAK and A BERNTSON*

Department of Electromagnetics, Chalmers University of Technology, SE-41296 Göteborg, Sweden

* Ericsson Telcom AB, SE-126 25 Stockholm, Sweden

Abstract.

A tutorial review is presented of the use of direct variational methods based on Rayleigh-Ritz optimization for finding approximate solutions to various nonlinear evolution equations. The practical application of the approach is demonstrated by some illustrative examples in connection with the nonlinear Schrödinger equation.

Keywords:  Variational method; Rayleigh-Ritz optimization; nonlinear Schrödinger equation; Euler--Lagrange equation; Bose--Einstein condensates; magnetic trap

Pacs Nos. 05.45Yv; 42.65.Tg