Geodesic
Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 2, pp. 233-241 
A. I. Zenchuk. Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 2, pp. 233-241. http://geodesic.mathdoc.fr/item/TMF_1997_110_2_a3/
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     author = {A. I. Zenchuk},
     title = {Some generalizations of the 2-dimensional {Toda} chain and $\operatorname{sh}${-Gordon} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {233--241},
     year = {1997},
     volume = {110},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_2_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the discrete transformations of the solutions and potentials of the second order partial differential equation with two independent variables. These transformations are introduced by the formula $D=V_1\partial_x+V_2\partial_y+V_3$. The simplest closed chains of these transformations are considered. The integrability of the derived nonlinear equations by the IST-method is proved.

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