Painleve type reductions for the non-Abelian Volterra lattices*

The Volterra lattice admits two non-Abelian analogs that preserve the integrability property. For each of them, the stationary equation for non-autonomous symmetries defines a constraint that is consistent with the lattice and leads to Painleve-type equations. In the case of symmetries of low order, including the scaling and master-symmetry, this constraint can be reduced to second order equations. This gives rise to two non-Abelian generalizations for the discrete Painleve equations and and for the continuous Painleve equations P-3, and P-5.

Automated summary

The Volterra lattice has two non-Abelian analogs that maintain integrability, with constraints that can be reduced to second order equations for low order symmetries, leading to Painleve-type equations. This results in two non-Abelian generalizations for discrete Painleve equations and continuous Painleve equations P-3 and P-5.