  It is known that inhomogeneous second-order macroscopic traffic models can
reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic
condition is violated, uniform traffic flow is unstable, and small
perturbations grow into nonlinear traveling waves, called jamitons. In
contrast, what is essentially unstudied is the question: which jamiton
solutions are dynamically stable? To understand which stop-and-go traffic waves
can arise through the dynamics of the model, this question is critical. This
paper first presents a computational study demonstrating which types of
jamitons do arise dynamically, and which do not. Then, a procedure is presented
that characterizes the stability of jamitons. The study reveals that a critical
component of this analysis is the proper treatment of the perturbations to the
shocks, and of the neighborhood of the sonic points.
