  We consider a hamiltonian system on the real line, consisting of real scalar
field $\phi(x,t)$ and point particle with trajectory $y(t)$. The dynamics of
this system is defined by the system of two equations: wave equation for the
field, <<radiated>> by the point particle, and Newton's equation for the
particle in its own field. We find the solution where the particle is strongly
damped, but the kinetic and interaction energies of the field increase linearly
in time, in despite of the full energy conservation.
