On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146092 |
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| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609029569708032 |
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| author | Golenia, J. Pavlov, M.V. Popowicz, Z. Prykarpatsky, A.K. |
| author_facet | Golenia, J. Pavlov, M.V. Popowicz, Z. Prykarpatsky, A.K. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-28T18:44:02Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146092 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T18:44:02Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Golenia, J. Pavlov, M.V. Popowicz, Z. Prykarpatsky, A.K. 2019-02-07T12:32:10Z 2019-02-07T12:32:10Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 35C05; 37K10 https://nasplib.isofts.kiev.ua/handle/123456789/146092 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability Article published earlier |
| spellingShingle | On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability Golenia, J. Pavlov, M.V. Popowicz, Z. Prykarpatsky, A.K. |
| title | On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability |
| title_full | On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability |
| title_fullStr | On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability |
| title_full_unstemmed | On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability |
| title_short | On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability |
| title_sort | on a nonlocal ostrovsky–whitham type dynamical system, its riemann type inhomogeneous regularizations and their integrability |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146092 |
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