-----------------------------------------------------------
Applied Mathematics Colloquium
Friday, March 27, 11:30 am
Cullimore Lecture Hall II
New
-----------------------------------------------------------
The Explosive Instability
Harvey Segur
Department of Applied Mathematics
Abstract
The "explosive instability" was discovered forty years ago by Coppi, Rosenbluth & Sudan
(1969) in a nonlinear, nondissipative
model of plasma physics. They showed that under the right conditions,
three wave trains that interact nonlinearly in a resonant
triad can all gain energy from a
background source, and all three waves can blow up together in finite
time. This can occur even if
the initial wave amplitudes were
quite small initially (hence the name "explosive instability"). Their argument was based on a
simplified version of their
mathematical model that omitted all spatial
dependence. More recently, Safdi & Segur (2007) showed
that
an explosive instability can occur
even in systems with no resonant triad interactions, because of resonant
quartets (involving four wave
trains) - again, all four wave
trains gain energy from a background source, and all blow up in finite
time. This talk will explain how
both processes work, and also show
that the instability is not quenched by spatial variation in the initial data,
or by (weak)
dissipation. No prior knowledge of the subject will be assumed.