Geodesic
Matrix Liouville equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 1, pp. 41-50

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Generalization of Liouville's equation to the case when the unknown function is a matrix is considered. For it, a Bicklund transformation is constructed and used to find several exact solutions. The question of the linear problem for such a matrix equation is discussed. 
@article{TMF_1990_83_1_a4,
     author = {V. A. Andreev},
     title = {Matrix {Liouville} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {41--50},
     publisher = {mathdoc},
     volume = {83},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a4/}
}
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V. A. Andreev. Matrix Liouville equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 1, pp. 41-50. http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a4/