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

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.

The probability density function tail of the Kardar–Parisi–Zhang equation in the strongly non-linear regime

“…Furthermore, the coefficients in the time evolution of the instanton will be dependent on the choice of structure. This is to elucidate on the machinery providing the scaling behavior and the PDFs [39][40][41].…”

“…Regarding the Burgers equation and the KPZ equations, the PDF has been computed in a similar manner previously in [33][34][35][36][37][38][39][40][41], however all these results relies on the assumption of a weakly non-linear system. In the present setting we focus on the effects in the intermittent or strongly non-linear regime where the extremal solution dominates the behavior and scaling of the system in the long time limit.…”