Integrable Bi-Hamiltonian Systems by Jacobi Structure on Real Three-Dimensional Lie Groups

Abstract

By Poissonization of Jacobi structures on real three-dimensional Lie groups $${\textbf{G}}$$ G and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $${\textbf{G}} \otimes {\mathbb {R}}$$ G ⊗ R .