Abstract
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.
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Acknowledgments
The authors are grateful to E. Ferapontov, A. Meshkov, and P. Leal da Silva for the useful discussions.
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This research was supported in part by the Russian state assignment No. 0033-2019-0006 and the State Program of the Ministry of Education and Science of the Russian Federation (Project No. 1.12873.2018/12.1).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 3, pp. 492–501, March, 2020.
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Sokolov, V.V. Integrable evolution systems of geometric type. Theor Math Phys 202, 428–436 (2020). https://doi.org/10.1134/S0040577920030149
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DOI: https://doi.org/10.1134/S0040577920030149