2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80992In 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.Drach23 pages; in RussianExactly Solvable and Integrable Systemstext