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Rational KdV Potentials and Differential Galois Theory
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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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, spectral curves
Mots-clés : Darboux transformations, rational solitons. 
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Sonia Jiménez; Juan J. Morales-Ruiz; Raquel Sánchez-Cauce; María-Ángeles Zurro. Rational KdV Potentials and Differential Galois Theory. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a46/

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