Hc. Chang et al., STABILITY OF A SOLITARY PULSE AGAINST WAVE-PACKET DISTURBANCES IN AN ACTIVE MEDIUM, Physical review letters, 75(9), 1995, pp. 1747-1750
Solitary pulses in an active medium, like those for the Kuramoto-Sivas
hinsky 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 e
xpanding wave packets. We show that this pulse-packet interaction is d
etermined by the essential spectrum of the pulse and a pulse stability
theory can be derived from a simple extension of the classical convec
tive instability theory for a wave packet on the trivial state.