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Algebra i Analiz, 2022, Volume 34, Issue 6, Pages 170–196 (Mi aa1839)  
Research Papers

Dubrovin method and Toda lattice

V. B. Matveevab, A. O. Smirnovc

a С.-Петербургское отделение Математического института им. В. А. Стеклова РАН, наб. р. Фонтанки, 27, 191023, Санкт-Петербург, Россия
b de Bourgogne, Université de Bourgogne, 9 Av. Alain Savary, 21078 Dijon, France
c С.-Петербургский государственный университет аэрокосмического приборостроения, ул. Б. Морская, 67а, 190000, Санкт-Петербург, Россия
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Abstract: A hierarchy of Lax pairs with $2\times2$ matrix coefficients is constructed. The compatibility conditions of these pairs include the Toda chain and other differential-difference integrable systems. Finite-gap solutions of these systems are constructed. Examples of the simplest one-phase and two-phase solutions and their corresponding spectral curves are given.
Keywords: Toda lattice, Lax pair, theta functions, finite-gap solutions, spectral curve.
Funding agency Grant number
Russian Science Foundation 22-11-00196
Received: 13.06.2022
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 6, Pages 1019–1037
DOI: https://doi.org/10.1090/spmj/1787
Document Type: Article
Language: Russian
Citation: V. B. Matveev, A. O. Smirnov, “Dubrovin method and Toda lattice”, Algebra i Analiz, 34:6 (2022), 170–196; St. Petersburg Math. J., 34:6 (2023), 1019–1037
Citation in format AMSBIB
\Bibitem{MatSmi22}
\by V.~B.~Matveev, A.~O.~Smirnov
\paper Dubrovin method and Toda lattice
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 6
\pages 170--196
\mathnet{http://mi.mathnet.ru/aa1839}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 6
\pages 1019--1037
\crossref{https://doi.org/10.1090/spmj/1787}
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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