Differential Galois theory and Darboux transformations for Integrable Systems

We apply the Differential Galois Theory of linear partial differential systems to the Bäcklund–Darboux transformations of the AKNS solitonic partial differential equations. We prove that the Galois group of the transformed system is isomorphic to a subgroup of the Galois group of the initial system....

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Detalles Bibliográficos
Autores: Jiménez, Sonia, Morales-Ruiz, Juan J., Sánchez-Cauce, Raquel, Zurro Moro, Ángeles
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/710648
Acceso en línea:http://hdl.handle.net/10486/710648
https://dx.doi.org/10.1016/j.geomphys.2016.06.016
Access Level:acceso abierto
Palabra clave:darboux transformations
differential Galois theory
integrability
Picard–Vessiot theory
solitons
Matemáticas
Descripción
Sumario:We apply the Differential Galois Theory of linear partial differential systems to the Bäcklund–Darboux transformations of the AKNS solitonic partial differential equations. We prove that the Galois group of the transformed system is isomorphic to a subgroup of the Galois group of the initial system. As an example, we study the integrability in closed form of the linear systems corresponding to the solitonic solutions of KdV equation