Spectral properties of polar operators with finite-gap elliptic densities

Abstract

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