  In this work we investigate the existence of non-monotone traveling wave
solutions to a reaction-diffusion system modeling social outbursts, such as
rioting activity, originally proposed in arXiv:1502.04725v3. The model consists
of two scalar values, the level of unrest $u$ and a tension field $v$. A key
component of the model is a bandwagon effect in the unrest, provided the
tension is sufficiently high. We focus on the so-called tension inhibitive
regime, characterized by the fact that the level of unrest has a negative
feedback on the tension. This regime has been shown to be physically relevant
for the spatiotemporal spread of the 2005 French riots. We use Geometric
Singular Perturbation Theory to study the existence of such solutions in two
situations. The first is when both $u$ and $v$ diffuse at a very small rate.
Here, the time scale over which the bandwagon effect is observed plays a key
role. The second case we consider is when the tension diffuses at a much slower
rate than the level of unrest. In this case, we are able to deduce that the
driving dynamics are modeled by the well-known Fisher-KPP equation.
