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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| Datum: | 2012 |
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| Sprache: | English |
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Інститут математики НАН України
2012
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/148455 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations / P.B. Acosta-Humánez. C. Pantazi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 46 назв. — англ. |
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irk-123456789-1484552019-02-19T01:23:23Z Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations Acosta-Humánez, P.B. Pantazi, C. 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. 2012 Article Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations / P.B. Acosta-Humánez. C. Pantazi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 12H05; 34A30; 34C14; 81Q60; 32S65 DOI: http://dx.doi.org/10.3842/SIGMA.2012.043 http://dspace.nbuv.gov.ua/handle/123456789/148455 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Acosta-Humánez, P.B. Pantazi, C. |
| spellingShingle |
Acosta-Humánez, P.B. Pantazi, C. Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Acosta-Humánez, P.B. Pantazi, C. |
| author_sort |
Acosta-Humánez, P.B. |
| title |
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations |
| title_short |
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations |
| title_full |
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations |
| title_fullStr |
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations |
| title_full_unstemmed |
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations |
| title_sort |
darboux integrals for schrödinger planar vector fields via darboux transformations |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148455 |
| citation_txt |
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations / P.B. Acosta-Humánez. C. Pantazi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 46 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT acostahumanezpb darbouxintegralsforschrodingerplanarvectorfieldsviadarbouxtransformations AT pantazic darbouxintegralsforschrodingerplanarvectorfieldsviadarbouxtransformations |
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2025-07-12T19:31:06Z |
| last_indexed |
2025-07-12T19:31:06Z |
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