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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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
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Abstract	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.]
AbstractList	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.] 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 Peer Reviewed 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.
Author	Acosta-Humánez, Primitivo B.
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Contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
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Copyright	Copyright National Academy of Sciences of Ukraine 2012 Attribution-NonCommercial-NoDerivs 3.0 Spain info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/3.0/es
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SubjectTerms	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
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Title	Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations
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