Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations

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 a...

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Bibliographic Details
Published in:Symmetry, integrability and geometry, methods and applications Vol. 8; p. 043
Main Author: Acosta-Humánez, Primitivo B.
Format: Journal Article Publication
Language:English
Published: Kiev National Academy of Sciences of Ukraine 01.01.2012
National Academy of Science of Ukraine
Subjects:
12 Field theory and polynomials
12H Differential and difference algebra
34 Ordinary differential equations
34A General theory
34C Qualitative theory
81 Quantum theory
81Q General mathematical topics and methods in quantum theory
Classificació AMS
Darboux theory of integrability
Darboux transformations
Differential equations
Differential Galois theory
Equacions diferencials
Equacions diferencials i integrals
Equacions diferencials ordinàries
Matemàtiques i estadística
Polinomis
Polynomials
Schrödinger equation
Supersymmetric quantum mechanics
Teoria de cossos i polinomis
Àlgebra
Àrees temàtiques de la UPC
ISSN:1815-0659, 1815-0659
Online Access:Get full text
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Summary: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. [ProQuest: [...] denotes formulae omitted.]
Bibliography:ObjectType-Article-1
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ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2012.043