%0 Journal Article
%T Darboux Integrals for Schr dinger Planar Vector Fields via Darboux Transformations
%A Primitivo B. Acosta-Hum¨˘nez
%A Chara Pantazi
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X In this paper we study the Darboux transformations of planar vector fields of Schr dinger 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.
%K Darboux theory of integrability
%K Darboux transformations
%K differential Galois theory
%K Schr dinger equation
%K supersymmetric quantum mechanics
%U http://dx.doi.org/10.3842/SIGMA.2012.043