Simple wave-like solutions to a class of hyperbolic models

A reduction method is worked out for determining exact solutions to quasilinear hyperbolic systems of first order PDEs involving two dependent and two independent variables as well as source-like terms. These governing models are related to hyperbolic dissipative theories where wave hierarchy problems must be taken into account. The approach in point is based upon appending suitable constraint equation to the set of balance laws to be satisfied by the dependent field variables. The resulting ansatz generalizes that one of classical simple wave solutions and, as far as wave hierarchies are concerned, it is able to characterize a higher order description of the wave process. Within the present theoretical framework exact solutions to traffic flow models are obtained.