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 Schrödinger equation defined at space dimensions exceeding a critical value. The so-called ‘‘strong’’ collapse, for which the mass of a collapsing solution remains concentrated near its central self-similar core, is shown to be characterized by an unstable contraction rate as time reaches the collapse singularity. By contrast with this latter case, a so-called ‘‘weak’’ collapse, whose mass dissipates into an asymptotic tail, is proven to contain a stable attractor from which a physical self-similar collapse may be realized.