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An invariant dierential-geome tric approach to the integrability of (2 + 1)-dimensional systems of hydrodynamic type, ut +A(u)ux +B(u)uy = 0, is developed. We prove that the existence of special solutions known as 'double waves' is equivalent to the diagonalizability of an arbitrary matrix of the two-parameter family

The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability