D.E. Pelinovsky and V.I. Shrira
Collapse transformation for self-focusing solitary waves in
boundary-layer type shear flows
Physics Letters A 206, 195-202 (1995)
Abstract:
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 self-similar
manner. The
explicit ''critical'' collapse transformation
of 2D solitons is found within the framework of
the Whitham adiabatic approach.