Poisson groups and differential Galois theory of Schroedinger equation on the circle

2007/10/29 by Ian Marshall, Michael Semenov-Tian-Shansky · 2 citations
Physics and Astronomy · Mathematics · #nlin.SI #math.QA

paper · pdf · doi:10.1007/s00220-008-0539-9

17 pages, LaTeX, XY-pic package used

arxiv created 2007/10/29 · arxiv updated 2009/12/01

Abstract

We combine the projective geometry approach to Schroedinger equations on the circle and differential Galois theory with the theory of Poisson Lie groups to construct a natural Poisson structure on the space of wave functions (at the zero energy level). Applications to KdV-like nonlinear equations are discussed. The same approach is applied to second order difference operators on a one-dimensional lattice, yielding an extension of the lattice Poisson Virasoro algebra.

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