Geodesic
Riccati scheme for integrating nonlinear systems of differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 352-363

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A modification of the Riccati system that makes it possible to reduce to linear problems the initial-value problem for systems of ordinary differential equations with bilinear nonlinearity is discussed. It is shown that from the algebraic point of view it is natural, in the framework of the scheme, to consider functions that take values in an algebra with two multiplications related by a condition of the type of associativity. 
@article{TMF_1995_102_3_a3,
     author = {A. Ya. Kazakov},
     title = {Riccati scheme for integrating nonlinear systems of differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {352--363},
     publisher = {mathdoc},
     volume = {102},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_3_a3/}
}
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A. Ya. Kazakov. Riccati scheme for integrating nonlinear systems of differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 352-363. http://geodesic.mathdoc.fr/item/TMF_1995_102_3_a3/