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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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149185 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491852019-02-20T01:23:33Z Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases Maltsev, A.Y. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149185 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Maltsev, A.Y. |
| spellingShingle |
Maltsev, A.Y. Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Maltsev, A.Y. |
| author_sort |
Maltsev, A.Y. |
| title |
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT maltsevay whithamsmethodanddubrovinnovikovbracketinsinglephaseandmultiphasecases |
| first_indexed |
2023-05-20T17:31:41Z |
| last_indexed |
2023-05-20T17:31:41Z |
| _version_ |
1796153492883111936 |