  In analogy to gas-dynamical detonation waves, which consist of a shock with
an attached exothermic reaction zone, we consider herein nonlinear traveling
wave solutions, termed "jamitons," to the hyperbolic ("inviscid") continuum
traffic equations. Generic existence criteria are examined in the context of
the Lax entropy conditions. Our analysis naturally precludes traveling wave
solutions for which the shocks travel downstream more rapidly than individual
vehicles. Consistent with recent experimental observations from a periodic
roadway (Sugiyama et al., New Journal of Physics, 10, 2008), our numerical
calculations show that, under appropriate road conditions, jamitons are
attracting solutions, with the time evolution of the system converging towards
a jamiton-dominated configuration. Jamitons are characterized by a sharp
increase in density over a relatively compact section of the roadway.
Applications of our analysis to traffic modeling and control are examined by
way of a detailed example.
