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...
Saved in:
Published in | Open Communications in Nonlinear Mathematical Physics Vol. Special Issue in Memory of... |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
International Society of Nonlinear Mathematical Physics
15.02.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |