  A relative motion of the normal and superfluid components of Helium II
results in Kelvin-Helmholtz instability (KHI) at their common free surface. We
found the exact solutions for the nonlinear stage of the development of that
instability. Contrary to the usual KHI of the interface between two fluids, the
dynamics of Helium II free surface allows decoupling of the governing equations
with their reduction to the Laplace growth equation which has the infinite
number of exact solutions including the formation of sharp cusps at free
surface in a finite time.
