The conservation of the Hamiltonian structures in Whitham's method of averaging

Details The conservation of the Hamiltonian structures in Whitham's method of averaging The conservation of the Hamiltonian structures in Whitham's method of averaging

1996-11-28

arxiv.org/abs/solv-int/9611008v2

Izvestiya, Mathematics 63:6 (1999), 1171-1201

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, some improvement, corrected misprints

Scientific paper

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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