AMS :: St. Petersburg Mathematical Journal

Dubrovin method and the Toda chain
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by V. B. Matveev and A. O. Smirnov;
Translated by: the authors

St. Petersburg Math. J. 34 (2023), 1019-1037

DOI: https://doi.org/10.1090/spmj/1787

Published electronically: January 26, 2024

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Abstract:

A hierarchy of Lax pairs with $2\times 2$ matrix coefficients is presented. The compatibility conditions for these pairs include the Toda chain equation, and other differential-difference integrable systems. Various kinds of finite gap solutions for such systems are constructed. Examples of simplest one- and two-phase solutions are given, together with the corresponding spectral curves.

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