Geodesic
Integrable equations for the partition function of the six vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 207-215 Cet article a éte moissonné depuis la source Math-Net.Ru

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The partition function of the six vertex model with the domain wall boundary condition is considered in the homogeneous and inhomogeneous cases. The determinant representation allows to show that the partition function is a solution of the Toda equation in the homogeneous case and solution of the Hirota equation in the inhomogeneous case. 
@article{ZNSL_1997_245_a10,
     author = {A. G. Izergin and E. Karjalainen and N. A. Kitanin},
     title = {Integrable equations for the partition function of the six vertex model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--215},
     year = {1997},
     volume = {245},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a10/}
}
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A. G. Izergin; E. Karjalainen; N. A. Kitanin. Integrable equations for the partition function of the six vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 207-215. http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a10/