Aspects of the Noisy Burgers Equation

TL;DR

This paper analyzes the one-dimensional noisy Burgers equation, revealing its growth morphology as a dilute soliton gas with specific scaling behavior using the Martin-Siggia-Rose technique.

Contribution

It provides a novel analysis of the growth morphology and scaling behavior of the noisy Burgers equation through a canonical formulation and spectral representation.

Findings

Growth morphology characterized by a dilute gas of nonlinear solitons

Scaling exponent z=3/2 identified

Heuristic expression for the scaling function derived

Abstract

The noisy Burgers equation describing for example the growth of an interface subject to noise is one of the simplest model governing an intrinsically nonequilibrium problem. In one dimension this equation is analyzed by means of the Martin-Siggia-Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The growth morphology is characterized by a dilute gas of nonlinear soliton modes with gapless dispersion law with exponent z=3/2 and a superposed gas of diffusive modes with a gap. The scaling exponents and a heuristic expression for the scaling function follow from a spectral representation.