Exact solutions of the time-dependent Schroedinger equation with self-consistent potential

Description of integrable models associated with a time-dependent Schroedinger equation is given along with constructing their multisoliton formulae. Among such models there are the vector versions of NLS, Yajima-Okiawa model and others. In constructing exact solutions the communication relations are not used. The condensate boundary conditions are considered for noncompact models where the conventional technique of the inverse transform is not effective. The proposed approach is based on the algebro-geometrical theory of integrable systems and allows to construct all known by now exact solutions of such systems. The review contains a number of original results and is addressed to nonmathematicians