Negative flows and non-autonomous reductions of the Volterra lattice
Abstract
We study reductions of the Volterra lattice corresponding to stationary equations for the additional, noncommutative subalgebra of symmetries. It is shown that, in the case of general position, such a reduction is equivalent to the stationary equation for a sum of the scaling symmetry and the negative flows, and is written as $(m+1)$-component difference equations of the Painlevé type generalizing the dP$_1$ and dP$_{34}$ equations. For these reductions, we present the isomonodromic Lax pairs and derive the Bäcklund transformations which form the $\mathbb{Z}^m$ lattice.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.08127
- arXiv:
- arXiv:2307.08127
- Bibcode:
- 2023arXiv230708127A
- Keywords:
-
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics
- E-Print:
- 17 pages. This article is part of an OCNMP Special Issue in Memory of Professor Decio Levi