Geodesic
Integrable evolution systems of geometric type
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 492-501

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We present necessary conditions for the integrability of multicomponent third-order evolution systems of geometric type. For the considered examples, the affine connected space determining the system turns out to be symmetric in the case of zero torsion. In the case of the connection with nonzero torsion, the space is generated by a Bol loop.
Keywords: integrable system, symmetry, affine connected space. 
@article{TMF_2020_202_3_a13,
     author = {V. V. Sokolov},
     title = {Integrable evolution systems of geometric type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {492--501},
     publisher = {mathdoc},
     volume = {202},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a13/}
}
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V. V. Sokolov. Integrable evolution systems of geometric type. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 492-501. http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a13/