Rational KdV Potentials and Differential Galois Theory
In this work, using differential Galois theory, we study the spectral problem of the one-dimensional Schrödinger equation for rational time-dependent KdV potentials. In particular, we compute the fundamental matrices of the linear systems associated with the Schrödinger equation. Furthermore, we pro...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210175 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Rational KdV Potentials and Differential Galois Theory / S. Jiménez, J.J. Morales-Ruiz, R. Sánchez-Cauce, M.-Á. Zurro // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In this work, using differential Galois theory, we study the spectral problem of the one-dimensional Schrödinger equation for rational time-dependent KdV potentials. In particular, we compute the fundamental matrices of the linear systems associated with the Schrödinger equation. Furthermore, we prove the invariance of the Galois groups with respect to time, to generic values of the spectral parameter, and to Darboux transformations.
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| ISSN: | 1815-0659 |