Geodesic
The Liouville equation and the lattice sinh-Gordon model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 7, Tome 161 (1987), pp. 24-44

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We show that the lattice Liouville model i s equivalent to a massl e s s version of the lattice Sinh-Gordon model. This allows to include the Liouville equation into the class of systems treatable by the quantum inverse scattering method. We also present a Hamiltonian for the quantum lattice Liouville model. 
@article{ZNSL_1987_161_a2,
     author = {A. Yu. Volkov},
     title = {The {Liouville} equation and the lattice {sinh-Gordon} model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {24--44},
     publisher = {mathdoc},
     volume = {161},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_161_a2/}
}
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A. Yu. Volkov. The Liouville equation and the lattice sinh-Gordon model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 7, Tome 161 (1987), pp. 24-44. http://geodesic.mathdoc.fr/item/ZNSL_1987_161_a2/