Stability of a Solitary Pulse against Wave Packet Disturbances in an Active Medium

Abstract

Solitary pulses in an active medium, like those for the Kuramoto-Sivashinsky equation for thin falling films, are often destroyed by growing and expanding wave packets from localized disturbances. The stability of a solitary pulse is then determined by whether is can escape the expanding wave packets. We show that this pulse-packet interaction is determined by the essential spectrum of the pulse and a pulse stability theory can be derived from a simple extension of the classical convective instability theory for a wave packet on the trivial state.