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 to the Schrödinger equation. Furthermore we prove...

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Detalles Bibliográficos
Autores: Jim Énez, Sonia, Morales-Ruiz, Juan J., Sánchez-Cauce, Raquel, Zurro Moro, Ángeles
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/691483
Acceso en línea:http://hdl.handle.net/10486/691483
https://dx.doi.org/10.3842/SIGMA.2019.047
Access Level:acceso abierto
Palabra clave:Darboux transformations
Differential Galois theory
KdV hierarchy
Rational solitons
Schrödinger operator
Spectral curves
Matemáticas
Descripción
Sumario: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