Instantons in the Burgers equation

The instanton solution for the forced Burgers equation is found. This solution describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent; that is, for large positive velocity differences. The results agree with the one found recently by Polyakov, who used the operator product conjecture. If this conjecture is true, then our WKB asymptotics of the Wyld functional integral should be exact to all orders of perturbation expansion around the instanton solution. We also generalized our solution for the arbitrary dimension of the Burgers (KPZ) equation. As a result we found the asymptotics of the angular dependence of the velocity difference probability distribution function. \textcopyright{} 1996 The American Physical Society.