Scaling function for the noisy Burgers equation in the soliton approximation

TL;DR

This paper derives the scaling function for the 1D noisy Burgers equation using a two-soliton approximation, confirming previous heuristic results and laying groundwork for many-body correlation analysis.

Contribution

It introduces a novel derivation of the scaling function within the two-soliton approximation using the weak noise phase space approach.

Findings

The derived scaling function agrees with earlier heuristic expressions.

The approach confirms correct scaling properties.

First step towards a many-body correlation treatment.

Abstract

We derive the scaling function for the one dimensional noisy Burgers equation in the two-soliton approximation within the weak noise canonical phase space approach. The result is in agreement with an earlier heuristic expression and exhibits the correct scaling properties. The calculation presents the first step in a many body treatment of the correlations in the Burgers equation.