STABILITY AND EVOLUTION OF THE QUIESCENT AND TRAVELING SOLITONIC BUBBLES

We simulate numerically the dynamics of the bubble-like solitons of th e cubic-quintic nonlinear Schrodinger equation. In agreement with earl ier predictions, slow moving bubbles have been observed to be unstable , in contrast to rapid bubbles which stabilize above a certain critica l velocity. The empirical formula for the critical velocity has been c onfirmed to a high degree of accuracy. Based on the choice of some cri tical perturbation, we derive an integral criterion for stability of k inks and bubbles of the general nonlinear Schrodinger equation which p rovides an explanation of the appearance of the critical velocity. Fin ally, we follow numerically the nonlinear evolution of the unstable bu bbles in one, two and three dimensions.