Аннотация:
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.
Ключевые слова:generalized Riemann type hydrodynamical equations; Whitham typedynamical systems; Hamiltonian systems; Lax type integrability;gradient-holonomic algorithm.