Analytical Properties of an Ostrovsky-Whitham Type Dynamical System for a Relaxing Medium with Spatial Memory and its Integrable Regularization
Exactly Solvable and Integrable Systems
2009-02-26 v1
Abstract
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 two- and four-dimensional invariant reductions are studied in detail. The well defined regularization of the model is constructed and its Lax type integrability is discussed.
Cite
@article{arxiv.0902.4395,
title = {Analytical Properties of an Ostrovsky-Whitham Type Dynamical System for a Relaxing Medium with Spatial Memory and its Integrable Regularization},
author = {Nikolai Bogolubov and Anatoliy Prykarpatsky and Ilona Gucwa and Jolanta Golenia},
journal= {arXiv preprint arXiv:0902.4395},
year = {2009}
}
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