Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles

I. M. Krichever, S. P. Novikov

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

Higher-rank solutions of the equations of the two-dimensionalized Toda lattice are constructed. The construction of these solutions is based on the theory of commuting difference operators, which is developed in the first part of the paper. It is shown that the problem of recovering the coefficients of commuting operators can be effectively solved by means of the equations of the discrete dynamics of the Tyurin parameters characterizing the stable holomorphic vector bundles over an algebraic curve.

Original languageEnglish
Pages (from-to)473-510
Number of pages38
JournalRussian Mathematical Surveys
Volume58
Issue number3
DOIs
Publication statusPublished - May 2003

Fingerprint

Dive into the research topics of 'Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles'. Together they form a unique fingerprint.

Cite this