Integrable Systems and Metrics of Constant Curvature
نویسنده
چکیده
PACS : 02.30.J, 11.10.E; MSC : 35L65, 35L70, 35Q35, 58F05, 58F07 keywords: Lagrangian, metrics of constant curvature, Hamiltonian structure, reciprocal transformation, Poisson brackets. Abstract. In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature. Kaup-Boussinesq system has three local Hamiltonian structures and one nonlocal Hamiltonian structure associated with metric of constant curvature. Darboux theorem (reducing Hamiltonian structures to canonical form ”d/dx” by differential substitutions and reciprocal transformations) for these Hamiltonian structures is proved.
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