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arxiv: 1108.4208 · v1 · pith:GXB3GLAKnew · submitted 2011-08-21 · 🌊 nlin.SI · math.DS

On integrability of the Kontsevich non-abelian ODE system

Thomas Wolf , Olga Efimovskaya This is my paper
classification 🌊 nlin.SI math.DS
keywords kontsevichsystemintegrabilityintegralsunknownsarbitrarycommutingconsider
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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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