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

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dc.contributor.authorGolenia, J.
dc.contributor.authorPavlov, M.V.
dc.contributor.authorPopowicz, Z.
dc.contributor.authorPrykarpatsky, A.K.
dc.date.accessioned2019-02-07T12:32:10Z
dc.date.available2019-02-07T12:32:10Z
dc.date.issued2010
dc.description.abstractShort-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.sponsorshipThis 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.identifier.citationOn 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.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 35C05; 37K10
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/146092
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleOn a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrabilityuk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6, випуск за цей рік