STABILITY AND EVOLUTION OF THE QUIESCENT AND TRAVELING SOLITONIC BUBBLES

We simulate numerically the dynamics of the bubble-like solitons of the cubic-quintic nonlinear Schrodinger equation. In agreement with earlier predictions, slow moving bubbles have been observed to be unstable, in contrast to rapid bubbles which stabilize above a certain critical velocity. The empirical formula for the critical velocity has been confirmed to a high degree of accuracy. Based on the choice of some critical perturbation, we derive an integral criterion for stability of kinks and bubbles of the general nonlinear Schrodinger equation which provides an explanation of the appearance of the critical velocity. Finally, we follow numerically the nonlinear evolution of the unstable bubbles in one, two and three dimensions.