Canonical phase-space approach to the noisy Burgers equation

Presenting a general phase-space approach to stochastic processes we analyz e in particular the Fokker-Planck equation for the noisy Burgers equation a nd discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the sym metric stationary Gaussian distribution. In the short-time regime we discus s heuristically the nonlinear soliton contributions and derive an expressio n for the distribution in accordance with the directed polymer-replica mode l and asymmetric exclusion model results. [S1063-651X(99)00710-2].