Noncommutative generalization of integrable quadratic ODE systems
Abstract
We find all homogeneous quadratic systems of ODEs with two dependent variables that have polynomial first integrals and satisfy the KowalevskiLyapunov test. Such systems have infinitely many polynomial infinitesimal symmetries. We describe all possible noncommutative generalizations of these systems and their symmetries. As a result, new integrable quadratic homogeneous systems of ODEs with two noncommutative variables are constructed. Their integrable noncommutative inhomogeneous generalizations are found. In particular, a noncommutative generalization of a Hamiltonian flow on the elliptic curve is presented.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 October 2019
 DOI:
 10.1007/s11005019012290
 arXiv:
 arXiv:1807.05583
 Bibcode:
 2019LMaPh.110..533S
 Keywords:

 Noncommutative ODEs;
 Integrability;
 Symmetries;
 Painlevé test;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 37K10;
 34M55
 EPrint:
 19 pages