Some Bi-Hamiltonian Equations in $R^3$

Abstract

Hamiltonian formulation of N=3 systems is considered in general. The Jacobi equation is solved in three classes. Compatible Poisson structures in these classes are determined and explicitly given. The corresponding bi-Hamiltonian systems are constructed and some explicit examples are given.

25 pages

References in corpus (3)

• New solutions of the Jacobi equations for three-dimensional Poisson structures
• A constant of motion in 3D implies a local generalized Hamiltonian structure
• One solution of the 3D Jacobi identities allows determining an infinity of them

Cited by in corpus (21)

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