Geodesic
On the complete integrability of a nonlinear system of partial differential equations in two-dimensional space
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 343-349 
A. N. Leznov. On the complete integrability of a nonlinear system of partial differential equations in two-dimensional space. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 343-349. http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the system of nonlinear partial differential equations of the form $$ \rho_{\alpha,z\bar z}=\sum_{\beta=1}^rk_{\alpha\beta}\exp\rho_\beta $$ where $k$ is the Cartan matrix of a certain semisimple algebra of the rank $r$, the complete integrability is demonstrated by means of constructing the complete solutions in an explicit form which depend on $2r$ arbitrary functions.

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