Rational KdV Potentials and Differential Galois Theory

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• Main Authors: Jiménez, S., Morales-Ruiz, J.J., Sánchez-Cauce, R., Zurro, M.-Á.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210175
• 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.

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...