Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups

Abstract

In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix for this family of bi-Hamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.

Keywords

• integrable system
• bi-hamiltonian
• control matrix
• variables of separation