Stability of the Travelling Front of a Decaying Brane

TL;DR

This paper investigates the stability of traveling front solutions in a non-local reaction-diffusion equation modeling tachyon dynamics on an unstable brane within a dilaton background, finding the front to be stable despite unstable modes.

Contribution

It provides a linearized stability analysis of traveling front solutions in a non-local reaction-diffusion equation related to brane tachyon dynamics, revealing stability properties.

Findings

Traveling front solutions are stable under linear perturbations.

Unstable modes exist around the (meta-)stable vacuum despite front stability.

Singular perturbation method yields stable front solutions.

Abstract

The dynamics (in light-cone time) of the tachyon on an unstable brane in the background of a dilaton linear along a null coordinate is a non-local reaction-diffusion type equation, which admits a travelling front solution. We analyze the (in-)stability of this solution using linearized perturbation theory. We find that the front solution obtained in singular perturbation method is stable. However, these inhomogenous solutions (unlike the homogenous solution) also have Lyapunov exponents corresponding to unstable modes around the (meta-)stable vacuum.