On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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dc.contributor.author	Golenia, J.
dc.contributor.author	Pavlov, M.V.
dc.contributor.author	Popowicz, Z.
dc.contributor.author	Prykarpatsky, A.K.
dc.date.accessioned	2019-02-07T12:32:10Z
dc.date.available	2019-02-07T12:32:10Z
dc.date.issued	2010
dc.identifier.citation	On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability / J. Golenia // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 35C05; 37K10
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146092
dc.description.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 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.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Proceedings of the Eighth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2009.html. M.P. and A.P. are appreciated to Organizers of the Symmetry-2009 Conference (June 21–27, 2009) held in Kyiv, Ukraine, and the NEEDS-2009 Conference (May 15–23, 2009), held in Isola Rossa of Sardinia, Italy, for the invitations to deliver reports and for partial support. M.P. was, in part, supported by RFBR grant 08-01-00054 and a grant of the RAS Presidium “Fundamental Problems of Nonlinear Dynamics”. The author's thanks go to Professors M. B laszak, N. Bogolubov (jr.) and D. Blackmore for useful discussions of the results obtained. Authors are also cordially thankful to Referees who have read the article and made very important remarks and suggestions, which were very instrumental for final preparing a manuscript, and which made it possible both to improve and correct the exposition.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA