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Short-wave perturbations in a relaxing medium, governed by a specialreduction of the Ostrovsky evolution equation, and later derived by Whitham,are studied using the gradient-holonomic integrability algorithm.Thebi-Hamiltonicity and complete integrability of the corresponding dynamicalsystem is stated and an infinite hierarchy of commuting to each otherconservation laws of dispersive type are found. The two- and four-dimensionalinvariant reductions are studied in detail. The well defined regularization ofthe model is constructed and its Lax type integrability is discussed.

Analytical Properties of an Ostrovsky-Whitham Type Dynamical System for a Relaxing Medium with Spatial Memory and its Integrable Regularization