Historical remarks to finite-gap integration theory: elementary treatment of the theory
Abstract
Description
In the example of the Schrödinger/KdV equation we give elementary treatment of the theory of finite-gap integration. The concept is equivalent to two kinds of Liouvillian integrability: quadrature integrability of linear differential equations with a parameter (spectral problem) and Liouville's integrability of finite-dimensional Hamiltonian systems (stationary KdV--equations).
Three key objects in this field: the new explicit formula for the $Ψ$-function, trace formula and the Jacobi problem provide a complete solution.
Appendix contains Russian translation of two papers of J.Drach
23 pages; in Russian
23 pages; in Russian