Canonical phase space approach to the noisy Burgers equation

Abstract

Presenting a general phase 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.

4 pages, Revtex file, submitted to Phys. Rev. Lett. a reference has been added and a few typos corrected

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Cited by in corpus (9)

• The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
• Power laws and stretched exponentials in a noisy finite-time-singularity model
• Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
• Solitons in the noisy Burgers equation
• Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions
• Correlations, soliton modes, and non-Hermitian linear mode transmutation in the 1D noisy Burgers equation
• Nonequilibrium dynamics of a growing interface
• Damped finite-time-singularity driven by noise
• Scaling function for the noisy Burgers equation in the soliton approximation