Geometry and Integrability in Mathematical Physics GIMP'06
May 15 - 19, 2006, Moscow, Russia
Alexei Penskoi
Independent University of Moscow & BMSTU
Laplace transformations and spectral theory of 2D semi-discrete hyperbolic Schr\"odinger operators.
We introduce Laplace transformations of 2D semi-discrete hyperbolic Schr\"odinger operators and show their relation to a semi-discrete 2D Toda lattice. We develop the algebro-geometric spectral theory of these operators and investigate spectral properties of the Laplace transformations. This makes it possible to find solutions of the semi-discrete 2D Toda lattice in terms of theta-functions.
Joint work (IMRN, 2006) with A. Oblomkov (IAS, Princeton).
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