  Instanton calculations are performed in the context of stationary Burgers
turbulence to estimate the tails of the probability density function (PDF) of
velocity gradients. These results are then compared to those obtained from
massive direct numerical simulations (DNS) of the randomly forced Burgers
equation. The instanton predictions are shown to agree with the DNS in a wide
range of regimes, including those that are far from the limiting cases
previously considered in the literature. These results settle the controversy
of the relevance of the instanton approach for the prediction of the velocity
gradient PDF tail exponents. They also demonstrate the usefulness of the
instanton formalism in Burgers turbulence, and suggest that this approach may
be applicable in other contexts, such as 2D and 3D turbulence in compressible
and incompressible flows.
