Integrable Systems and Metrics of Constant Curvature

Details Integrable Systems and Metrics of Constant Curvature Integrable Systems and Metrics of Constant Curvature

2001-11-05

arxiv.org/abs/nlin/0111013v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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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