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

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

2007-10-29

arxiv.org/abs/0710.5456v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, LaTeX, XY-pic package used

Scientific paper

10.1007/s00220-008-0539-9

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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