Nonstable solitons and sharp criteria for wave collapse

Sharp sufficient criteria for collapse are found for the nonlinear Schr\"odinger equation in the so-called supercritical case as well as for the Ginzburg-Landau equation in the case of the subcritical bifurcation. It is demonstrated that nonstable solitons in these models, under some additional assumptions, play the role of a ``boundary'' (saddle points) between collapsing and noncollapsing solutions.