Geodesic
The Drinfeld--Sokolov reduction for a Lax difference operator with the periodic boundary conditions in the case $gl\bigl(n,\mathbb C((\lambda^{-1}))\bigr)$
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 15, Tome 251 (1998), pp. 233-259

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Matrix difference equations of a special kind are investigated by means of the dressing equations method. It is shown that these equations are gauge invariant, the corresponding flows being commutative. It is proved that the equation for the gauge equivalence class and the Lax equation are equivalent. 
@article{ZNSL_1998_251_a15,
     author = {A. L. Pirozerskii},
     title = {The {Drinfeld--Sokolov} reduction for a {Lax} difference operator with the periodic boundary conditions in the case $gl\bigl(n,\mathbb C((\lambda^{-1}))\bigr)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {233--259},
     publisher = {mathdoc},
     volume = {251},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_251_a15/}
}
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A. L. Pirozerskii. The Drinfeld--Sokolov reduction for a Lax difference operator with the periodic boundary conditions in the case $gl\bigl(n,\mathbb C((\lambda^{-1}))\bigr)$. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 15, Tome 251 (1998), pp. 233-259. http://geodesic.mathdoc.fr/item/ZNSL_1998_251_a15/