Hodograph transformation and differential constraints for wave solutions to 2 × 2 quasilinear hyperbolic nonhomogeneous systems

The differential constraint method is used to work out a reduction approach to determine solutions in a closed form to the highly nonlinear hodograph system arising from 2×2 hyperbolic nonhomogeneous models. These solutions inherit all of the features of the standard wave solutions obtainable via the classical hodograph transformation and in the meantime incorporate the dissipative effects induced on wave processes by the source-like term involved in the governing equations. Within such a theoretical framework the problem of integrating the standard linear hodograph system associated with 2 × 2 homogeneous models is also revisited and a number of results obtained elsewhere of relevant interest in wave problems are recovered as a particular case. Along the lines of the proposed reduction approach, different examples of 2 × 2 governing models are analysed thoroughly in order to highlight the flexibility of the provided solutions to describe hyperbolic dissipative wave processes.