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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 047, 40 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.047 (Mi sigma1483) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Rational KdV Potentials and Differential Galois Theory

Sonia Jiméneza, Juan J. Morales-Ruizb, Raquel Sánchez-Caucec, María-Ángeles Zurroc

a Junta de Castilla y León, Salamanca, Spain
b Departamento de Matemática Aplicada, E.T.S. Edificación, Universidad Politécnica de Madrid, Madrid, Spain
c Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
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DOI: https://doi.org/10.3842/SIGMA.2019.047
URL: https://www.imath.kiev.ua/~sigma/2019/047/
Abstract: 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.
Keywords: differential Galois theory, KdV hierarchy, Schrödinger operator, Darboux transformations, spectral curves, rational solitons.
Received: September 11, 2018; in final form May 29, 2019; Published online June 25, 2019
Bibliographic databases:
Document Type: Article
MSC: 12H05, 35Q51, 37K10
Language: English
Citation: Sonia Jiménez, Juan J. Morales-Ruiz, Raquel Sánchez-Cauce, María-Ángeles Zurro, “Rational KdV Potentials and Differential Galois Theory”, SIGMA, 15 (2019), 047, 40 pp.
Citation in format AMSBIB
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\paper Rational KdV Potentials and Differential Galois Theory
\jour SIGMA
\yr 2019
\vol 15
\papernumber 047
\totalpages 40
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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