Wave collapse in plasmas and fluids

This lecture is a review of recent results (obtained mainly by the author and his co-authors) in the wave collapse theory with applications to plasma physics, fluid dynamics and nonlinear optics as well. The main attention in the review is paid to the qualitative reasons of the wave collapse and to the exact methods based on the integral estimations. Both approaches are applied to both the nonlinear Schrodinger equation and the two-dimensional generalized Benjamin-Ono equation which describes self-focusing of low-frequency oscillations in the boundary layer.