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Darboux integrals for Schrödinger planar vector fields via Darboux transformations

Autor
Acosta, P.; Pantazi, C.
Tipus d'activitat
Article en revista
Revista
Symmetry, integrability and geometry: methods and applications
Data de publicació
2012-07-14
Pàgina inicial
1
Pàgina final
26
DOI
https://doi.org/10.3842/SIGMA.2012.043 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/16689 Obrir en finestra nova
Resum
In this paper we study the Darboux transformations of planar vector fields of Schr odinger type. Using the isogaloisian property of Darboux transformation we prove the \invariance" of the objects of the \Darboux theory of integrability". In particular, we also show how the shape invariance property of the potential is important in order to preserve the structure of the transformed vector field. Finally, as illustration of these results, some examples of planar vector fields coming from supersymm...
Citació
Acosta, P.; Pantazi, C. Darboux integrals for Schrödinger planar vector fields via Darboux transformations. "Symmetry, integrability and geometry: methods and applications", 14 Juliol 2012, p. 1-26.
Paraules clau
Darboux theory of integrability, Darboux transformations, Differential Galois theory, Schrödinger equation, Supersymmetric quantum mechanics
Grup de recerca
SD - Sistemes Dinàmics de la UPC

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