# Wavenumber Selection in Pattern Forming Systems

## TL;DR

This paper demonstrates through extensive numerical simulations that noise acts as a robust mechanism for selecting a unique wavenumber in pattern forming systems, independent of initial conditions or noise strength.

## Contribution

It provides the first large-scale numerical evidence supporting noise-induced wavenumber selection in the stabilized Kuramoto-Sivashinsky equation.

## Key findings

- Unique wavenumber state has highest probability at long times
- Wavenumber selection is independent of noise strength
- State is robust against initial conditions

## Abstract

Wavenumber selection in pattern forming systems remains a long standing puzzle in physics. Previous studies have shown that external noise is a possible mechanism for wavenumber selection. We conduct an extensive numerical study of the noisy stabilized Kuramoto Sivashinsky equation. We use a fast spectral method of integration, which enables us to investigate long time behavior for large system sizes that could not be investigated by earlier work. We find that a state with a unique wavenumber has the highest probability of occurring at very long times. We also find that this state is independent of the strength of the noise and initial conditions, thus making a convincing case for the role of noise as a mechanism of state selection.