Dynamics of correlations in atomic Bose-Einstein condensates

The Gross-Pitaevskii equation has been extremely successful in the theory of weakly-interacting Bose-Einstein condensates. However, present-day experiments reach beyond the regime of its validity due to the significant role of correlations. We review a method of tackling the dynamics of correlations in Bose condensed gases, in terms of noncommutative cumulants. This new approach has a wide range of applicability in the areas of current interest, e.g. the production of molecules and the manipulation of interactions in condensates. It also offers an interesting perspective on the classical-field methods for partly condensed Bose gases.