Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds

2000/03/10 by S. P. Novikov, I. A. Dynnikov · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Russian Math. Surveys 52 (1997), no. 5, 1057--1116 · LaTeX, 66 pages

arxiv created 2000/03/10 · arxiv updated 2009/11/30

Abstract

Euler-Darboux-Backlund and Laplace transformations are considered for the one- and two-dimensional Schrodinger operators. Their discrete analogs are constructed and generalized for the multidimensional lattices and two-manifolds with special "black-white" triangulations. Nonstandard generalizations of the connections and curvature are constructed for the simplicial complexes. Exactly solvable 2D Schrodinger operators with nonstandard spectral properties are constructed in the continuous and discrete cases using Laplace chains with different restrictions.

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• Darboux formulae for linear hyperbolic equations in discrete case

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