  Based on an approach introduced byGerjuoy, Rau, and Spruch, we constract
variational principles in a systematic way for the nonlinear Schroedinger
equation and obtain new variational principles for the case of
Ginzburg-Pitaevskii-Gross equation (PGP) which is belived to describe
accurately the Bose-Einstein condensation at zero temperature. As an
application of these variational methods, a variational iteration method is
proposed for calculating eigenvalue (chemical potential) and wave function for
the GPG equation
