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
Pages 10
Keywords integrability, Laurent ODEs, matrix ODEs, Lax pairs, computer algebra
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.
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