Publication: On integrability of the Kontsevich non-abelian ODE system

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Title	On integrability of the Kontsevich non-abelian ODE system
Authors/Editors*	T Wolf, O Efimovskaya
Where published*	submitted to Letters of Math Phys
How published*	Journal
Year*	2011
Volume
Number
Pages	10
Publisher
Keywords	integrability, Laurent ODEs, matrix ODEs, Lax pairs, computer algebra
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Abstract	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.