Correlations, soliton modes, and non-Hermitian linear mode transmutation in the 1D noisy Burgers equation

TL;DR

This paper investigates the complex growth patterns and mode behaviors in the 1D noisy Burgers equation, revealing how solitons influence mode transmutation and non-Hermitian spectral properties.

Contribution

It provides a detailed analysis of nonlinear soliton modes, linear mode transmutation, and the non-Hermitian spectrum in the noisy Burgers equation using a canonical phase space approach.

Findings

Identification of mode transmutation from diffusive to propagating

Analysis of correlations in multi-soliton sectors

Insights into anomalous diffusion and scaling properties

Abstract

Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multi-soliton sector, and in detail the correlations and scaling properties in the two-soliton sector.