The averaging of nonlocal Hamiltonian structures in Whitham's method
We consider the m-phase Whitham's averaging method and propose the procedure of averaging nonlocal Hamiltonian structures. The procedure is based on the existence of a sufficient number of local-commuting integrals of the system and gives the Poisson bracket of Ferapontov type for Whitham'...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202106120 |
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| _version_ | 1850223581417439232 |
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| author | Andrei Ya. Maltsev |
| author_facet | Andrei Ya. Maltsev |
| author_sort | Andrei Ya. Maltsev |
| collection | DOAJ |
| description | We consider the m-phase Whitham's averaging method and propose the procedure of averaging nonlocal Hamiltonian structures. The procedure is based on the existence of a sufficient number of local-commuting integrals of the system and gives the Poisson bracket of Ferapontov type for Whitham's system. The method can be considered as the generalization of the Dubrovin-Novikov procedure for the local field-theoretical brackets. |
| format | Article |
| id | doaj-art-48d4f12e81674c28a03901854fe348b5 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-48d4f12e81674c28a03901854fe348b52025-08-20T02:05:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130739943410.1155/S0161171202106120The averaging of nonlocal Hamiltonian structures in Whitham's methodAndrei Ya. Maltsev0Landau Institute for Theoretical Physics, 117940, Kosygina 2, Moscow, RussiaWe consider the m-phase Whitham's averaging method and propose the procedure of averaging nonlocal Hamiltonian structures. The procedure is based on the existence of a sufficient number of local-commuting integrals of the system and gives the Poisson bracket of Ferapontov type for Whitham's system. The method can be considered as the generalization of the Dubrovin-Novikov procedure for the local field-theoretical brackets.http://dx.doi.org/10.1155/S0161171202106120 |
| spellingShingle | Andrei Ya. Maltsev The averaging of nonlocal Hamiltonian structures in Whitham's method International Journal of Mathematics and Mathematical Sciences |
| title | The averaging of nonlocal Hamiltonian structures in Whitham's method |
| title_full | The averaging of nonlocal Hamiltonian structures in Whitham's method |
| title_fullStr | The averaging of nonlocal Hamiltonian structures in Whitham's method |
| title_full_unstemmed | The averaging of nonlocal Hamiltonian structures in Whitham's method |
| title_short | The averaging of nonlocal Hamiltonian structures in Whitham's method |
| title_sort | averaging of nonlocal hamiltonian structures in whitham s method |
| url | http://dx.doi.org/10.1155/S0161171202106120 |
| work_keys_str_mv | AT andreiyamaltsev theaveragingofnonlocalhamiltonianstructuresinwhithamsmethod AT andreiyamaltsev averagingofnonlocalhamiltonianstructuresinwhithamsmethod |