Rational KdV Potentials and Differential Galois Theory

Symmetry Integrability and Geometry-Methods and Applications

article

Sonia Jiménez¹  Juan J. Morales-Ruiz²  Raquel Sánchez-Cauce³  María-Ángeles Zurro³ 

[1] Junta de Castilla y León; Universidad Politécnica de Madrid;Universidad Autónoma de Madrid

关键词: differential Galois theory;    KdV hierarchy;    Schr¨odinger operator;    Darboux transformations;    spectral curves;    rational solitons;   

DOI  :  10.3842/SIGMA.2019.047

来源: National Academy of Science of Ukraine

【 摘 要 】

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 to 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.

【 授权许可】

Unknown