Two-dimensional discrete operators and rational functions on algebraic curves
Exactly Solvable and Integrable Systems
2025-01-24 v1 Algebraic Geometry
Abstract
In this paper we study a connection between finite-gap on one energy level two-dimensional Schrodinger operators and two-dimensional discrete operators. We find spectral data for a new class of two-dimensional integrable discrete operators. These operators have eigenfunctions on zero level energy parameterized by points of algebraic spectral curves. In the case of genus one spectral curves we show that the finite-gap Schrodinger operators can be obtained as a limit of the discrete operators.
Cite
@article{arxiv.2501.13539,
title = {Two-dimensional discrete operators and rational functions on algebraic curves},
author = {Polina A. Leonchik and Andrey E. Mironov},
journal= {arXiv preprint arXiv:2501.13539},
year = {2025}
}
Comments
16 pages