2005/04/24 by Yu. V. Brezhnev, Brezhnev, Yu. V.
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0504051
23 pages; in Russian
arxiv created 2005/04/24 · arxiv updated 2009/12/01
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