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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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Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
Інший ID:
2010 Mathematics Subject Classification: 37K05; 35B10; 35B15; 35B34; 35L65
DOI: http://dx.doi.org/10.3842/SIGMA.2012.103
DOI: http://dx.doi.org/10.3842/SIGMA.2012.103
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
428
Завантажень:
195
Анотація:
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.
