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arXiv · 2307.08127

Negative flows and non-autonomous reductions of the Volterra lattice

V. E. Adler
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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 Painlev\'e type generalizing the dP$_1$ and dP$_{34}$ equations. For these reductions, we present the isomonodromic Lax pairs and derive the B\"acklund transformations which form the $\mathbb{Z}^m$ lattice.

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V. E. Adler. 2023-07-16. Negative flows and non-autonomous reductions of the Volterra lattice. https://doi.org/10.46298/ocnmp.11597

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