Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations

Symmetry Integrability and Geometry-Methods and Applications

article

Primitivo B. Acosta-Humánez¹  Chara Pantazi² 

[1] Departamento de Matemáticas y Estadística Universidad del Norte;Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya

关键词: Darboux theory of integrability;    Darboux transformations;    dif ferential Galois theory;    Schr¨odinger equation;    supersymmetric quantum mechanics;   

DOI  :  10.3842/SIGMA.2012.043

来源: National Academy of Science of Ukraine

【 摘 要 】

In this paper we study the Darboux transformations of planar vector fields of Schrödinger 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.

【 授权许可】

Unknown