Painlevé type reductions for the non-Abelian Volterra lattices *
- 29 December 2020
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 54 (3) , 035204
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 and and for the continuous Painlevé equations P 3 , and P 5 .Keywords
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