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Russian Mathematical Surveys, 2011, Volume 66, Issue 1, Pages 107–144
DOI: https://doi.org/10.1070/RM2011v066n01ABEH004729 (Mi rm9403) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Singular spectral curves in finite-gap integration

I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
English version PDF (742 kB) Citations (9)
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DOI: https://doi.org/10.1070/RM2011v066n01ABEH004729
Abstract: A number of examples of applications of the method of finite-gap integration of non-linear equations are considered in which singular spectral curves occur. In particular, constructions of orthogonal curvilinear coordinate systems for which a reducible spectral curve consists of rational components are discussed, along with constructions of finite-gap Frobenius manifolds, and a soliton deformation of spectral curves is demonstrated which consists in the creation and annihilation of singular points and corresponds to equations with self-consistent sources.
Bibliography: 52 titles.
Keywords: finite-gap integration, non-linear equations, Riemann surfaces, singular algebraic curves.
Received: 01.12.2010
Russian version:
Uspekhi Matematicheskikh Nauk, 2011, Volume 66, Issue 1(397), Pages 111–150
DOI: https://doi.org/10.4213/rm9403
Bibliographic databases:
Document Type: Article
UDC: 517.957+517.22+514.83
MSC: Primary 37K20, 37K25; Secondary 35Q53
Language: English
Original paper language: Russian
Citation: I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Uspekhi Mat. Nauk, 66:1(397) (2011), 111–150; Russian Math. Surveys, 66:1 (2011), 107–144
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
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