Abstract:
 In this lecture, we consider the theory of dispersive shocks which can develop, instead of wellknown viscous shocks, in evolution of various physical systems, if dispersion effects dominate dissipative ones. After short discussion of examples of dispersive shocks which provide physical motivation for the theory, such modern mathematical methods as finitegap integration method of integration of completely integrable evolution equations, Whitham modulation theory and generalized hodograph method are briefly reviewed. These methods are illustrated by application to description of dispersive shocks in evolution of BoseEinstein condensates which is a topical subject of current research.
