Singular spectral curves in finite-gap integration

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.