2-DIMENSIONAL WAVE COLLAPSE IN THE BOUNDARY-LAYER

In the framework of the generalized two-dimensional Benjamin-Ono equation it is demonstrated both analytically and numerically that in the limit of small viscosity the instability of one-dimensional long-wave solitons in the boundary layer results in their self-focusing and collapse. The exact upper boundary for the total energy of perturbations is found when the collapse is still impossible and when any perturbation vanishes asymptotically in long time. Theoretical predictions are in qualitative agreement with the experiments.