PHYSICS LETTERS A Collapse transformation for self-focusing solitary waves in boundary-layer type shear flows

Evolution of long-wave weakly nonlinear two-dimensional perturbations in parallel boundary-layer type shear flows is considered within the model simplified by using the paraxial approximation. The transverse instability of 1D solitons is shown to result in formation of 2D collapsing clusters which evolve in a serf-similar manner. The explicit "critical" collapse transformation f 2D solitons is found within the framework of the Whitham adiabatic approach. 1. It is well-known (see, e.g. Ref. [1]) that the dynamics of solitary waves in various physical prob-lems being well described within the framework of approximate weakly nonlinear models often exhibits formation of amplitude singularities emerging in a certain finite time ("col lapse"), the more probable the higher dimension of the problem is. In the case of collapse, one may expect formation of a number of drastic effects depending on the specific physics of the problem. Within the hydrodynamics ontext, it may mean formation of strongly nonlinear large-am-plitude coherent structures from the small-amplitude solitary waves unstable with respect o self-focusing or wave breaking. The collapse is always character