  Exact solutions of a classical problem of a plane unsteady potential flow of
an ideal incompressible fluid with a free boundary are presented. The fluid
occupies a semi-infinite strip bounded by the free surface (from above) and
(from the sides) by two solid vertical walls approaching each other with a
constant velocity. The solutions are obtained for a situation where the
capillary and gravity forces are absent, and the fluid motion is completely
determined by the motion of the walls. The solutions contain an arbitrary
function, which allows one to describe the nonlinear evolution of perturbations
of an arbitrary shape for an initially flat horizontal surface of the fluid.
Examples of exact solutions corresponding to the formation of bubbles, cuspidal
points, and droplets are considered.
