Spectral properties of polar operators with finite-gap ellipticdensities

摘要

The higher-times approach to construction of finite-gap solutionsof the Harry Dim equation has been improved. It is based on an explicitrepresentation of conservation laws' fluxes as differential polynomials.In the stationary limit along with well-known smooth densities also somenew singular one- and two-gap densities of the polar operator associatedwith the Harry Dim equation have been built. The procedure of reductionof one- and two-gap densities into the soliton sector has been verified