Effective dynamics of solitons

It is a common understanding in Physics that dynamics at a given scale originate from dynamics on a finer scale. In this talk I will demonstrate how this works for the case of low energy solutions of the nonlinear Schrödinger and Hartree equations with external potentials. We show how the description of such solutions can be reduced to dynamics of rigidly moving well localized structures - solitons (ground states). I will review some recent results on and state open problems in this subject.