A reduction method to quasilinear hyperbolic systems of multicomponent field PDEs with application to wave interaction

A reduction method is worked out for determining a class of exact solutions with inherent wave features to quasilinear hyperbolic homogeneous systems of N > 2 first-order autonomous PDEs. A crucial point of the present approa ch is that in the process the original set of field equations induces the h yperbolicity of an auxiliary 2 x 2 subsystem and connection between the res pective characteristic velocities can be established. The integration of th is auxiliary subsystem via the hodograph method and through the use of the Riemann invariants provides the searched solutions to the full governing sy stem. These solutions also represent invariant solutions associated with gr oups of translation of space/time coordinates and involving arbitrary funct ions that can be used for studying non-linear wave interaction. Within such a theoretical framework the two-dimensional motion of an adiabatic fluid i s considered. For appropriate model pressure-entropy-density laws, we deter mine a solution to the governing system of equations which describes in the 2 + 1 space two non-linear waves which were initiated as plane waves, inte ract strongly on colliding but emerge with unaffected profile from the inte raction region, These model material laws include the classical pressure-en tropy-density law which is usually adopted for a polytropic fluid. (C) 2001 Elsevier Science Ltd. All rights reserved.