  An invariant differential-geometric approach to the integrability of
(2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=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.

Exactly Solvable and Integrable Systems