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This article is cited in 8 scientific papers (total in 8 papers)
Singular spectral curves in finite-gap integration
I. A. Taimanov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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
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
Linking options:
https://www.mathnet.ru/eng/rm9403https://doi.org/10.1070/RM2011v066n01ABEH004729 https://www.mathnet.ru/eng/rm/v66/i1/p111
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Abstract page: | 1157 | Russian version PDF: | 361 | English version PDF: | 18 | References: | 99 | First page: | 51 |
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