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Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations
Інший ID:
2010 Mathematics Subject Classification: 12H05; 34A30; 34C14; 81Q60; 32S65
DOI: http://dx.doi.org/10.3842/SIGMA.2012.043
DOI: http://dx.doi.org/10.3842/SIGMA.2012.043
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
772
Завантажень:
200
Анотація:
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.
