V. Gurarie et A. Migdal, INSTANTONS IN THE BURGERS-EQUATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(5), 1996, pp. 4908-4914
The instanton solution for the forced Burgers equation is found. This
solution describes the exponential tail of the probability distributio
n function of velocity differences in the region where shock waves are
absent; that is, or large positive velocity differences. The results
agree with the one found recently by Polyakov, who used thr operator p
roduct conjecture. If this conjecture is true, then our WKB asymptotic
s of the Wyld functional integral should be exact to all orders of per
turbation expansion around the instanton solution. We also generalized
our solution for the arbitrary dimension of the Burgers (KPZ) equatio
n. As a result we found the asymptotics of the angular dependence of t
he velocity difference probability distribution function.