  Multicomponent KdV-systems are defined in terms of a set of structure
constants and, as shown by Svinolupov, if these define a Jordan algebra the
corresponding equations may be said to be integrable, at least in the sense of
having higher-order symmetries, recursion operators and hierarchies of
conservation laws. In this paper the dispersionless limits of these Jordan KdV
equations are studied, under the assumptions that the Jordan algebra has a
unity element and a compatible non-degenerate inner product. Much of this
structure may be encoded in a so-called Jordan manifold, akin to a Frobenius
manifold. In particular the Hamiltonian properties of these systems are
investigated.
