The problem of parametric excitation of high-mode oscillations is solved fo
r a non-linear telegraph equation with a parametric external excitation and
small diffusion. The equation is considered on a finite (spatial) interval
with Neumann boundary conditions. It is shown that under a proper choice o
f parameters of the external excitation this boundary-value problem can hav
e arbitrarily many exponentially stable solutions that are periodic in time
and rapidly oscillate with respect to the spatial variable.