  A special asymptotic solution of the Painlev\'e-2 equation with small
parameter is studied. This solution has a critical point $t_*$ corresponding to
a bifurcation phenomenon. When $t<t_*$ the constructed solution varies slowly
and when $t>t_*$ the solution oscillates very fast. We investigate the
transitional layer in detail and obtain a smooth asymptotic solution, using a
sequence of scaling and matching procedures.
