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 |
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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| id |
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Jiménez, S. Morales-Ruiz, J.J. Sánchez-Cauce, R. Zurro, M.-Á. 2025-12-03T14:25:13Z 2019 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. 1815-0659 2010 Mathematics Subject Classification: 12H05; 35Q51; 37K10 arXiv: 1808.00743 https://nasplib.isofts.kiev.ua/handle/123456789/210175 https://doi.org/10.3842/SIGMA.2019.047 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. We kindly thank all members of the Integrability Madrid Seminar for many fruitful discussions: P. Acosta-Humánez, D. Blázquez, J.A. Capitán, R. Hernández Heredero, A. PérezRaposo, J. Rojo Montijano, and S. Rueda. The authors gratefully acknowledge the reviewers for their helpful comments and further references, which resulted in an improvement of the preliminary manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Rational KdV Potentials and Differential Galois Theory Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Rational KdV Potentials and Differential Galois Theory |
| spellingShingle |
Rational KdV Potentials and Differential Galois Theory Jiménez, S. Morales-Ruiz, J.J. Sánchez-Cauce, R. Zurro, M.-Á. |
| title_short |
Rational KdV Potentials and Differential Galois Theory |
| title_full |
Rational KdV Potentials and Differential Galois Theory |
| title_fullStr |
Rational KdV Potentials and Differential Galois Theory |
| title_full_unstemmed |
Rational KdV Potentials and Differential Galois Theory |
| title_sort |
rational kdv potentials and differential galois theory |
| author |
Jiménez, S. Morales-Ruiz, J.J. Sánchez-Cauce, R. Zurro, M.-Á. |
| author_facet |
Jiménez, S. Morales-Ruiz, J.J. Sánchez-Cauce, R. Zurro, M.-Á. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210175 |
| citation_txt |
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. |
| work_keys_str_mv |
AT jimenezs rationalkdvpotentialsanddifferentialgaloistheory AT moralesruizjj rationalkdvpotentialsanddifferentialgaloistheory AT sanchezcaucer rationalkdvpotentialsanddifferentialgaloistheory AT zurroma rationalkdvpotentialsanddifferentialgaloistheory |
| first_indexed |
2025-12-07T21:24:38Z |
| last_indexed |
2025-12-07T21:24:38Z |
| _version_ |
1850886249257107456 |