Nondiagonalizable Hydrodynamic Type Systems Integrable by Tsarev's Generalised Hodograph Method

We investigate integrability of nondiagonalizable hydrodynamic type systems.
In the simplest nontrivial case (2x2 Jordan blocks) we derive integrability conditions.
Two distinguish classes of solutions are selected:
1. linearly-degenerate case;
2. strongly-nonlinear case.
The first case belongs to the so-called Darboux integrable class. The second case belongs to MKP hierarchy.