A new Liouville transformation for the Geng-Xue system

We construct a new Liouville transformation for the Geng-Xue system and show that the associated Geng-Xue system is a reduction of the first negative flow in a modified Boussinesq hierarchy. Using this transformation, we consider the behaviors of the solutions and bi-Hamiltonian structures between the Geng-Xue and associated systems. We also give the infinitely many conserved quantities and prove the Painlevé property of the associated system.