Geodesic
A differential-geometric criterion of the kinematic integrability of nonlinear differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 247-254

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A theorem on the existence of a $G$-representation and a differential-geometric criterion of the kinematic integrability for nonlinear differential equations from the $\Lambda^2$-$G$-classes is proved. Examples of zero-curvature representations and metrics for some equations of mathematical physics are presented. 
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     title = {A differential-geometric criterion of the kinematic integrability of nonlinear differential equations},
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D. V. Tikhomirov; S. A. Zadadaev. A differential-geometric criterion of the kinematic integrability of nonlinear differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 247-254. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a12/