Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
Abstract
An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type ut+A(u)ux+B(u)uy=0 is developed. It is proved that the existence of special solutions known as `double waves' is equivalent to the diagonalizability of an arbitrary matrix of the two-parameter family (kE+A)-1(lE+B). Since the diagonalizability can be effectively verified by differential-geometric means, this provides a simple necessary condition for integrability.
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