TY - JOUR

T1 - Two-dimensional discrete operators and rational functions on algebraic curves

AU - Leonchik, Polina A.

AU - Mironov, Andrey E.

N1 - This work was supported by the Russian Science Foundation, project no. 24-11-00281.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper we study a connection between finite-gap on one energy level two-dimensional Schrödinger 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 Schrödinger operators can be obtained as a limit of the discrete operators.

AB - In this paper we study a connection between finite-gap on one energy level two-dimensional Schrödinger 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 Schrödinger operators can be obtained as a limit of the discrete operators.

KW - Baker–Akhiezer function

KW - Discrete operators

KW - Two-dimensional Schrödinger operator

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200046359&origin=inward&txGid=15dee66edbc180897befa2888ac7d85b

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001280680000001

UR - https://www.mendeley.com/catalogue/b89792f0-4f73-3b2e-9890-6f166d2365b9/

U2 - 10.1007/s40863-024-00455-2

DO - 10.1007/s40863-024-00455-2

M3 - Article

VL - 18

SP - 855

EP - 865

JO - Sao Paulo Journal of Mathematical Sciences

JF - Sao Paulo Journal of Mathematical Sciences

SN - 2316-9028

IS - 2

ER -