%0 Journal Article %T Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Haghighatdoost, Ghorbanali - %A Abdolhadi-Zangakani, Salahaddin %A Mahjoubi-Bahman, Rasoul %D 2021 %\ 02/01/2021 %V 18 %N 1 %P 89-105 %! Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups %K Integrable system %K Bi-Hamiltonian %K Control matrix %K Variables of separation %R 10.22130/scma.2020.122380.764 %X 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. %U https://scma.maragheh.ac.ir/article_239419_f6268693ead8255708129744af870e59.pdf