Singular spectral curves in finite-gap integration

I. A. Taimanov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 1, pp. 107-144

Résumé

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.

Détail

Keywords: finite-gap integration, non-linear equations, Riemann surfaces, singular algebraic curves.

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