  Coherent structures are solutions to reaction-diffusion systems that are
time-periodic in an appropriate moving frame and spatially asymptotic at
$x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned
with sources which are coherent structures for which the group velocities in
the far field point away from the core. Sources actively select wave numbers
and therefore often organize the overall dynamics in a spatially extended
system. Determining their nonlinear stability properties is challenging as
localized perturbations may lead to a non-localized response even on the linear
level due to the outward transport. Using a modified Burgers equation as a
model problem that captures some of the essential features of coherent
structures, we show how this phenomenon can be analysed and nonlinear stability
be established in this simpler context.
