Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs

Abstract

A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a $$2 \times 2$$ reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary $$2 \times 2$$ system. An example of interest to viscoelasticity is presented.