the nonlinear schrodinger equation, is an example of a dispersive wave equation which has many different asymptotic states depending on the initial data. such time dependent equations play a central role in many of the latestscientific advances,such as bose-einstein condensates and optical devices .i will discuss the solutions of such equations,including the large time behavior:first rigorous proof of the phenomena of ground state selection, asymptotic instability of the excited states and more.these results are obtained by deriving a novel nonlinear master equation and multitime scale analysis of its properties.the talk will be general.