Darboux integrals for Schrödinger planar vector fields via Darboux transformations

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Defense date2012-07-14
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Abstract
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 supersymmetric quantum mechanics are
studied
CitationAcosta, 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.
ISSN1815-0659
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