v 2 5 O ct 1 99 9 The conservation of the Hamiltonian structures in Whitham ’ s method of averaging
نویسنده
چکیده
The conservation of the Hamiltonian structures in Whitham's method of averaging. 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 Pois-son bracket, proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of restriction of the Poisson bracket on the subman-ifold 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.
منابع مشابه
Hydrodynamics of Weakly Deformed Soliton Lattices. Differential Geometry and Hamiltonian Theory Hydrodynamics of Weakly Deformed Soliton Lattices. Differential Geometry and Hamiltonian Theory
CONTENTS Introduction 35 Chapter I. Hamiltonian theory of systems of hydrodynamic type 45 § 1. General properties of Poisson brackets 45 §2. Hamiltonian formalism of systems of hydrodynamic type and 55 Riemannian geometry §3. Generalizations: differential-geometric Poisson brackets of higher orders, 66 differential-geometric Poisson brackets on a lattice, and the Yang-Baxter equation §4. Rieman...
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