Dubrovin method and the Toda chain
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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.References
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Bibliographic Information
- V. B. Matveev
- Affiliation: St. Petersburg Branch of V. A. Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia; and Institut de Mathematique de Bourgogne, Universite de Bourgogne, 9 Avenue Alain Savary, 21078 Dijon, France
- MR Author ID: 191115
- ORCID: 0000-0002-4607-7535
- Email: vladimir.matveev9@gmail.com
- A. O. Smirnov
- Affiliation: St. Petersburg State University of Aerospace Instrumentation, Bolshaya Morskaya, 67A, 190000 St. Petersburg, Russia
- ORCID: 0000-0002-6781-2105
- Email: alsmir@guap.ru
- Received by editor(s): June 13, 2022
- Published electronically: January 26, 2024
- Additional Notes: The authors appreciate the financial support provided by the Russian Science Foundation (grant agreement no. 22-11-00196)
- © Copyright 2024 American Mathematical Society
- Journal: St. Petersburg Math. J. 34 (2023), 1019-1037
- MSC (2020): Primary 37K10; Secondary 35Q53, 35Q55
- DOI: https://doi.org/10.1090/spmj/1787