  The equation of motion of a general class of macroscopic traffic flow models
is linearized around a steady uniform flow. A closed-form solution of a
boundary-initial value problem is obtained, and it is used to describe several
phenomena. Specifically, the scenarios examined involve a smooth velocity field
in stop-and-go traffic, a discontinuous velocity field with shock waves in a
traffic light problem, and discontinuous displacement fields in a problem where
a single platoon of vehicles splits into two, and later merges back into one.
