Integrable non-abelian quadratic ODEs

Vladimir Sokolov, Landau Institute for Theoretical Physics. Part of the integrable systems seminar.

We consider ODE systems with two variables, which are matrices of an arbitrary size. The RHS of the systems are assumed to be quadratic homogeneous. We obtain a list of integrable systems of this type.

It generalizes the results obtained by A. Mikhailov and V. Sokolov in "Integrable ODEs on Associative Algebras",CMP, 2000, Volume 211, Issue 1, pp 231–251.