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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2019
Автори: Jiménez, S., Morales-Ruiz, J.J., Sánchez-Cauce, R., Zurro, M.-Á.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2019
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/210175
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
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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.
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
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language English
last_indexed 2025-12-07T21:24:38Z
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spelling 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
spellingShingle Rational KdV Potentials and Differential Galois Theory
Jiménez, S.
Morales-Ruiz, J.J.
Sánchez-Cauce, R.
Zurro, M.-Á.
title 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_short Rational KdV Potentials and Differential Galois Theory
title_sort rational kdv potentials and differential galois theory
url https://nasplib.isofts.kiev.ua/handle/123456789/210175
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AT moralesruizjj rationalkdvpotentialsanddifferentialgaloistheory
AT sanchezcaucer rationalkdvpotentialsanddifferentialgaloistheory
AT zurroma rationalkdvpotentialsanddifferentialgaloistheory