Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
In this paper we examine in detail the procedure of averaging of the local field-theoretic Poisson brackets proposed by B.A. Dubrovin and S.P. Novikov for the method of Whitham. The main attention is paid to the questions of justification and the conditions of applicability of the Dubrovin-Novikov p...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149185 |
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| Cite this: | Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases / A.Y. Maltsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 50 назв. — англ. |
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Maltsev, A.Y. 2019-02-19T18:22:01Z 2019-02-19T18:22:01Z 2012 Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases / A.Y. Maltsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 50 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K05; 35B10; 35B15; 35B34; 35L65 DOI: http://dx.doi.org/10.3842/SIGMA.2012.103 https://nasplib.isofts.kiev.ua/handle/123456789/149185 In this paper we examine in detail the procedure of averaging of the local field-theoretic Poisson brackets proposed by B.A. Dubrovin and S.P. Novikov for the method of Whitham. The main attention is paid to the questions of justification and the conditions of applicability of the Dubrovin-Novikov procedure. Separate consideration is given to special features of single-phase and multiphase cases. In particular, one of the main results is the insensitivity of the procedure of bracket averaging to the appearance of ''resonances'' which can arise in the multi-phase situation. This paper is a contribution to the Special Issue “Geometrical Methods in Mathematical Physics”. The full collection is available at http://www.emis.de/journals/SIGMA/GMMP2012.html. In conclusion the author expresses his deep gratitude to Professors S.P. Novikov, B.A. Dubrovin, I.M. Krichever, S.Yu. Dobrokhotov, and M.V. Pavlov for fruitful discussions. This work was financially supported by the Russian Federation Government Grant No. 2010-220-01-077, Grant of the President of Russian Federation NSh-4995.2012.1, and Grant RFBR No. 11-01-12067-ofim-2011. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases |
| spellingShingle |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases Maltsev, A.Y. |
| title_short |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases |
| title_full |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases |
| title_fullStr |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases |
| title_full_unstemmed |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases |
| title_sort |
whitham's method and dubrovin-novikov bracket in single-phase and multiphase cases |
| author |
Maltsev, A.Y. |
| author_facet |
Maltsev, A.Y. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In this paper we examine in detail the procedure of averaging of the local field-theoretic Poisson brackets proposed by B.A. Dubrovin and S.P. Novikov for the method of Whitham. The main attention is paid to the questions of justification and the conditions of applicability of the Dubrovin-Novikov procedure. Separate consideration is given to special features of single-phase and multiphase cases. In particular, one of the main results is the insensitivity of the procedure of bracket averaging to the appearance of ''resonances'' which can arise in the multi-phase situation.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149185 |
| citation_txt |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases / A.Y. Maltsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 50 назв. — англ. |
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AT maltsevay whithamsmethodanddubrovinnovikovbracketinsinglephaseandmultiphasecases |
| first_indexed |
2025-11-29T01:49:00Z |
| last_indexed |
2025-11-29T01:49:00Z |
| _version_ |
1850854381723844608 |