Miura transformations for Toda--type integrable systems, with applications to the problem of integrable discretizations

1999/02/04 by Yuri B. Suris, Suris, Yuri B.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9902003

LaTeX, 58 pp

arxiv created 1999/02/04 · openalex publication_date 1999/02/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study lattice Miura transformations for the Toda and Volterra lattices, relativistic Toda and Volterra lattices, and their modifications. In particular, we give three successive modifications for the Toda lattice, two for the Volterra lattice and for the relativistic Toda lattice, and one for the relativistic Volterra lattice. We discuss Poisson properties of the Miura transformations, their permutability properties, and their role as localizing changes of variables in the theory of integrable discretizations.

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