Document Type : Research Paper


1 Department of Mathematics,Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran.

2 Department of Mathematics, University of Bonab, Tabriz, Iran.


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.


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