V. E. Adler - Negative flows and non-autonomous reductions of the Volterra lattice

ocnmp:11597 - Open Communications in Nonlinear Mathematical Physics, February 15, 2024, Special Issue in Memory of Decio Levi - https://doi.org/10.46298/ocnmp.11597
Negative flows and non-autonomous reductions of the Volterra latticeArticle

Authors: V. E. Adler

    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.


    Volume: Special Issue in Memory of Decio Levi
    Published on: February 15, 2024
    Accepted on: December 11, 2023
    Submitted on: July 18, 2023
    Keywords: Nonlinear Sciences - Exactly Solvable and Integrable Systems,Mathematical Physics

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