  Short-wave perturbations in a relaxing medium, governed by a special
reduction of the Ostrovsky evolution equation, and later derived by Whitham,
are studied using the gradient-holonomic integrability algorithm. The
bi-Hamiltonicity and complete integrability of the corresponding dynamical
system is stated and an infinite hierarchy of commuting to each other
conservation laws of dispersive type are found. The well defined regularization
of the model is constructed and its Lax type integrability is discussed. A
generalized hydrodynamical Riemann type system is considered, infinite
hierarchies of conservation laws, related compatible Poisson structures and a
Lax type representation for the special case N=3 are constructed.
