  For the problem of Burgers turbulence with random gaussian forcing a
similarity functional solution of Hopf equation is presented and compared with
scaling arguments and replica Bethe-anzatz treatments. The corresponding field
theory is almost non-anomalous. In one dimension the local fluctuations develop
self-similar time-dependent behavior, while relative fluctuations within the
correlation length form a steady-state with gaussian distribution. This is the
precise meaning of the so-called fluctuation-dissipation theorem. The
one-dimensional properties are also studied numerically. It is shown that the
fluctuation-dissipation theorem is invalid above one dimension and higher-order
cumulants are non-zero. In two dimensions the cumulants exhibit logarithmic
spatial dependence which is close to but different from that in the
Edwards-Wilkinson case. No other similarity functional solution is found which
may indicate that the ``strong-coupling'' results are not described by Burgers
equation with gaussian noise.
