Hamiltonian Formalism of One-dimensional Systems of Hydrodynamic Type, and the Bogolyubov–whitman Averaging Method
نویسندگان
چکیده
Theorem 1. 1) Under local changes of the fields u = u(w) the coefficient g(u) in the bracket (2) transforms like a bilinear form (a tensor with upper indices); if det g 6= 0, then the expression b k (u) = gΓ j sk transforms in such a way that the Γjsk are the Christoffel tymbols of a differential-geometric connection. 2) In order that the bracket (2) be skew-symmetric it is necessary and sufficient that the tensor g(u) be symmetric (i.e., that it define a pseudo-Riemannian metric
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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