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Integrable Systems and Metrics of Constant Curvature

Maxim V. Pavlov
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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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Maxim V. Pavlov. 2001-11-05. Integrable Systems and Metrics of Constant Curvature. https://doi.org/10.2991/jnmp.2002.9.s1.15

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