Poisson Groups and Differential Galois Theory of Schroedinger Equation on the Circle

Ian Marshall1, Michael Semenov-Tian-Shansky2,3
1Mathematics Department, University of Loughborough, Loughborough, UK
2Steklov Mathematical Institute, St. Petersburg, Russia
3Institute Mathématique de Bourgogne, Dijon, France

Tóm tắt

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 2nd order difference operators on a one-dimensional lattice, yielding an extension of the lattice Poisson Virasoro algebra.

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