Linearly degenerate reducible systems of hydrodynamic type (Q1269047)

The author investigates strictly hyperbolic reducible systems of hydrodynamic type \[ u_{i,t}= \sum_j v_{ij}(u) u_{j,x},\quad i,j= 1,2,3. \] A complete description of such systems is presented. It is proved, that any such a system can be reduced to the scalar Monge-Ampère type equation of the third-order. The non-strict hyperbolic case of multiple characteristics is also considered. Finally, there are given the classification of scalar Monge-Ampère type equations and corresponding systems.