Generalized simple wave solutions to quasilinear hyperbolic nonhomogeneous systems of PDEs are obtained through the differential constraint method. These solutions prove to be flexible enough to solve generalized Riemann problems where discontinuous initial data are involved. Within such a theoretical framework, the governing model of nonlinear transmission lines is investigated throughout.

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Within the theoretical framework of differential constraints method a nonhomogeneous model describing traffic flows is considered. Classes of exact solutions to the governing equations under interest are determined. Furthermore, Riemann problems and generalized Riemann problems which model situations of interest for traffic flows are solved.

In this paper we present a new solution for the Constant Astigmatism equation. This solution is parameterized by an arbitrary function of a single variable.