Non-linear geometrical optics in the theory of evolution of waves in a plasma

Exact analytical solutions in non-linear dynamics of the large-scale localized distributions of the electromagnetic waves in plasma are discussed. In the framework of such solutions the dependence of the tendencies of the evolution on the initial form of the distribution is indicated. The formation of the peculiarities and the occurrence of new peaks in the course of evolution of an initially smooth wave's distributions are considered. (author)