Negative flows and non-autonomous reductions of the Volterra lattice

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 negati...

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Bibliographic Details
Published in:Open Communications in Nonlinear Mathematical Physics 2024-02, Vol.Special Issue in Memory of...
Main Author: Adler, V. E.
Format: Article
Language:English
Subjects:
mathematical physics
nonlinear sciences - exactly solvable and integrable systems
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Summary: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.
ISSN:2802-9356
2802-9356
DOI:10.46298/ocnmp.11597