It is known that a large class of integrable hydrodynamic type systems can be
constructed through the Lauricella function, a generalization of the classical
Gauss hypergeometric function. In this paper, we construct novel class of
integrable hydrodynamic type systems which govern the dynamics of critical
points of confluent Lauricella type functions defined on finite dimensional
Grassmannian Gr(2,n), the set of 2xn matrices of rank two. Those confluent
functions satisfy certain degenerate Euler-Poisson-Darboux equations. It is
also shown that in general, hydrodynamic type system associated to the
confluent Lauricella function is given by an integrable and non-diagonalizable
quasi-linear system of a Jordan matrix form. The cases of Grassmannian Gr(2,5)
for two component systems and Gr(2,6) for three component systems are
considered in details.Comment: 22 pages, PMNP 2015, added some comments and reference
