On the Dubrovin Equations for the Finite-gap Potentials

Abstract

The general technique of derivation of Dubrovin's equation for the arbitrary operator pencils is suggested. The question of unique recovering of the finite-gap potential by coordinates of zeroes of the Psi-function is discussed. The crucial result of the paper is an autonomous form of Dubrovin's equations and new trace-formulas for nontrivial spectral problems of the 3-rd order with trigonal algebraic curve. We show only demonstrative examples, the method is spread into arbitrary spectral problem including matrix ones.

4 pages, no figures