Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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dc.contributor.author	Maltsev, A.Y.
dc.date.accessioned	2019-02-19T18:22:01Z
dc.date.available	2019-02-19T18:22:01Z
dc.date.issued	2012
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 37K05; 35B10; 35B15; 35B34; 35L65
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.103
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149185
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	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	Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA