Geodesic
$q$-Discretization of the two-dimensional Toda equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 390-398

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$q$-Discrete versions of the two-dimensional Toda molecule equation and the two-dimensional Toda lattice equation are proposed through the direct method. Bäcklund transformation and Lax pair of the former are obtained. Moreover, reduction to the $q$-discrete cylindrical Toda equations is also discussed. 
@article{TMF_1994_99_3_a5,
     author = {K. Kajiwara and Ya. Ohta and J. Satsuma},
     title = {$q${-Discretization} of the two-dimensional {Toda} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {390--398},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a5/}
}
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K. Kajiwara; Ya. Ohta; J. Satsuma. $q$-Discretization of the two-dimensional Toda equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 390-398. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a5/