Painlevé type reductions for the non-Abelian Volterra lattices

Abstract

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 Painlevé-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 Painlevé equations dP${}_1$ and dP${}_{34}$ and for the continuous Painlevé equations P${}_3$, P${}_4$ and P${}_5$.

14 pages

References in corpus (1)

• Non-Abelian evolution systems with conservation laws

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