Morphology and scaling in the noisy Burgers equation: Soliton approach to the strong coupling fixed point

TL;DR

This paper investigates the morphology and scaling of the noisy Burgers equation in one dimension using a nonlinear soliton approach, revealing the strong coupling fixed point and describing the interface growth behavior.

Contribution

It introduces a soliton-based method to analyze the strong coupling fixed point of the noisy Burgers equation, providing new insights into its scaling and morphology.

Findings

Growth morphology described by a soliton gas

Dynamic exponent linked to soliton dispersion law

Scaling function resembles a Levy flight distribution

Abstract

The morphology and scaling properties of the noisy Burgers equation in one dimension are treated by means of a nonlinear soliton approach based on the Martin-Siggia-Rose technique. In a canonical formulation the strong coupling fixed point is accessed by means of a principle of least action in the asymptotic nonperturbative weak noise limit. The strong coupling scaling behaviour and the growth morphology are described by a gas of nonlinear soliton modes with a gapless dispersion law and a superposed gas of linear diffusive modes with a gap. The dynamic exponent is determined by the gapless soliton dispersion law, whereas the roughness exponent and a heuristic expression for the scaling function are given by the form factor in a spectral representation of the interface slope correlation function. The scaling function has the form of a Levy flight distribution.