Canonical phase-space approach to the noisy Burgers equation

Presenting a general phase-space approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short-time regime we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer-replica model and asymmetric exclusion model results.