Publication Date:
2020-12-11
Description:
We consider systems of ODEs with the right hand side being Laurent
polynomials in several non-commutative unknowns. In particular,
these unknowns could be matrices of arbitrary size. An important
example of such a system was proposed by M. Kontsevich. We prove the
integrability of the Kontsevich system by finding a Lax pair,
corresponding first integrals and commuting flows. We also provide
a pre-Hamiltonian operator which maps gradients of integrals for
the Kontsevich system to symmetries.
Language:
English
Type:
reportzib
,
doc-type:preprint
Format:
application/pdf
Format:
application/postscript
Permalink