DYNAMICAL STABILITY ANALYSIS OF STRONG WEAK WAVE COLLAPSES

The dynamical stability of self-similar wave collapses is investigated in the framework of the radially symmetric nonlinear Schrodinger equa tion defined at space dimensions exceeding a critical value. The so-ca lled ''strong'' collapse, for which the mass of a collapsing solution remains concentrated near its central self-similar core, is shown to b e characterized by an unstable contraction rate as time reaches the co llapse singularity. By contrast with this latter case, a so-called ''w eak'' collapse, whose mass dissipates into an asymptotic tail, is prov en to contain a stable attractor from which a physical self-similar co llapse may be realized.