A Unified Construction of Variational Methods for the Nonlinear Schroedinger Equation

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