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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148455 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862739996964814848 |
|---|---|
| author | Acosta-Humánez, P.B. Pantazi, C. |
| author_facet | Acosta-Humánez, P.B. Pantazi, C. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T20:12:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148455 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:12:35Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Acosta-Humánez, P.B. Pantazi, C. 2019-02-18T12:57:39Z 2019-02-18T12:57:39Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148455 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. This paper is a contribution to the Special Issue “Geometrical Methods in Mathematical Physics”. The full collection is available at http://www.emis.de/journals/SIGMA/GMMP2012.html.
 The authors are partial supported by the MICINN/FEDER grant number MTM2009-06973. The first author is also supported by Research Department of Universidad del Norte grant Agenda 2012. CP is additionally partially supported by the MICINN/FEDER grant MTM2008–03437 and by the Generalitat de Catalunya grant number 2009SGR859. The authors acknowledge to the anonymous referees by their useful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations Article published earlier |
| spellingShingle | Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations Acosta-Humánez, P.B. Pantazi, C. |
| title | 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_short | Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations |
| title_sort | darboux integrals for schrödinger planar vector fields via darboux transformations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148455 |
| work_keys_str_mv | AT acostahumanezpb darbouxintegralsforschrodingerplanarvectorfieldsviadarbouxtransformations AT pantazic darbouxintegralsforschrodingerplanarvectorfieldsviadarbouxtransformations |