Geodesic
Complete integrability of the nonlinear ito and Benney--Kaup systems: Gradient algorithm and lax representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 67 (1986) no. 3, pp. 410-425

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A new gradient-holonomic approach to the construction of integrability criteria for nonlinear dynamical systems is described for the example of the nonlinear hydrodynamic equations in the mechanics of Ito and of Benney and Kaup. 
@article{TMF_1986_67_3_a6,
     author = {N. N. Bogolyubov (Jr.) and A. K. Prikarpatskii},
     title = {Complete integrability of the nonlinear ito and {Benney--Kaup} systems: {Gradient} algorithm and lax representation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {410--425},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_67_3_a6/}
}
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N. N. Bogolyubov (Jr.); A. K. Prikarpatskii. Complete integrability of the nonlinear ito and Benney--Kaup systems: Gradient algorithm and lax representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 67 (1986) no. 3, pp. 410-425. http://geodesic.mathdoc.fr/item/TMF_1986_67_3_a6/