Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface
Abstract We show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a $$2$$ -surface. In the case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker–Akhiezer function.
Authors
- S. V. Agapov (ORCID: https://orcid.org/0009-0009-4135-5792)
- Andrey E. Mironov (ORCID: https://orcid.org/0000-0003-4974-8530)
Institutions
- Novosibirsk State University (RU)
- Sobolev Institute of Mathematics (RU)
- Siberian Branch of the Russian Academy of Sciences (RU)
Publication Details
- Journal
- Proceedings of the Steklov Institute of Mathematics
- Published
- 2024-12-01
- DOI
- https://doi.org/10.1134/s0081543824060014
- Citations
- 1
- Primary Topic
- Nonlinear Waves and Solitons
- Type
- article
- Field-Weighted Citation Impact
- 0.28
Funders
- Russian Science Foundation