Integrable Systems and Metrics of Constant Curvature

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.

Cited by in corpus (6)

• Gurevich-Zybin system
• Algebro-geometric approach in the theory of integrable hydrodynamic type systems
• Integrable models for shallow water with energy dependent spectral problems
• Symmetry algebras of Lagrangian Liouville-type systems
• Algebraic properties of Gardner's deformations for integrable systems
• Gardner's deformations of the Boussinesq equations