dorsal/arxiv
View SchemaThe conservation of the Hamiltonian structures in Whitham's method of averaging
| Authors | A. Ya. Maltsev |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9611008 |
| URL | https://arxiv.org/abs/solv-int/9611008 |
| Journal | Izvestiya, Mathematics 63:6 (1999), 1171-1201 |
Abstract
The work is devoted to the proof of the conservation of local field-theoretical Hamiltonian structures in Whitham's method of averaging. The consideration is based on the procedure of averaging of local Poisson bracket, proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of restriction of the Poisson bracket on the submanifold in the functional space, it is shown in the generic case that the Poisson bracket, constructed by method of Dubrovin and Novikov, satisfies the Jacobi identity. Besides that, the invariance of this bracket with respect to the choice of the set of local conservation laws, used in this procedure, is proved.
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"abstract": "The work is devoted to the proof of the conservation of local\nfield-theoretical Hamiltonian structures in Whitham\u0027s method of averaging. The\nconsideration is based on the procedure of averaging of local Poisson bracket,\nproposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of\nrestriction of the Poisson bracket on the submanifold in the functional space,\nit is shown in the generic case that the Poisson bracket, constructed by method\nof Dubrovin and Novikov, satisfies the Jacobi identity. Besides that, the\ninvariance of this bracket with respect to the choice of the set of local\nconservation laws, used in this procedure, is proved.",
"arxiv_id": "solv-int/9611008",
"authors": [
"A. Ya. Maltsev"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"journal_ref": "Izvestiya, Mathematics 63:6 (1999), 1171-1201",
"title": "The conservation of the Hamiltonian structures in Whitham\u0027s method of averaging",
"url": "https://arxiv.org/abs/solv-int/9611008"
},
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