Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 54, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/abd21f
Keywords
non-Abelian system; symmetry; constraint; Volterra lattice; Painlevé equation; isomonodromic deformation; quasi-determinant
Categories
Funding
- Ministry of Science and Higher Education of the Russian Federation [0033-2019-0004]
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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.
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.
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