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SIGMA, 2012, Volume 8, 043, 26 pages (Mi sigma720)  

This article is cited in 5 scientific papers (total in 5 papers)

Darboux integrals for Schrödinger planar vector fields via Darboux transformations

Primitivo B. Acosta-Humáneza, Chara Pantazib

a Departamento de Matemáticas y Estadística Universidad del Norte, Km. 5 via Puerto Colombia, Barranquilla, Colombia
b Departament de Matemàtica Aplicada I, Universitat Politécnica de Catalunya, (EPSEB), Av. Doctor Marañón, 44-50, 08028 Barcelona, Spain

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.

Keywords: Darboux theory of integrability, Darboux transformations, differential Galois theory, Schrödinger equation, supersymmetric quantum mechanics.

DOI: https://doi.org/10.3842/SIGMA.2012.043

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Full text: http://emis.mi.ras.ru/.../043
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Bibliographic databases:

ArXiv: 1111.0120
MSC: 12H05; 34A30; 34C14; 81Q60; 32S65
Received: March 5, 2012; in final form July 6, 2012; Published online July 14, 2012
Language:

Citation: Primitivo B. Acosta-Humánez, Chara Pantazi, “Darboux integrals for Schrödinger planar vector fields via Darboux transformations”, SIGMA, 8 (2012), 043, 26 pp.

Citation in format AMSBIB
\Bibitem{AcoPan12}
\by Primitivo B. Acosta-Hum\'anez, Chara Pantazi
\paper Darboux integrals for Schr\"odinger planar vector fields via Darboux transformations
\jour SIGMA
\yr 2012
\vol 8
\papernumber 043
\totalpages 26
\mathnet{http://mi.mathnet.ru/sigma720}
\crossref{https://doi.org/10.3842/SIGMA.2012.043}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2958987}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306353200001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864831396}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Morales-Ruiz J.J., “Picard-Vessiot Theory and Integrability”, J. Geom. Phys., 87 (2015), 314–343  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Acosta-Humanez P.B., Tomas Lazaro J., Morales-Ruiz J.J., Pantazi Ch., “On the Integrability of Polynomial Vector Fields in the Plane By Means of Picard-Vessiot Theory”, Discret. Contin. Dyn. Syst., 35:5 (2015), 1767–1800  crossref  mathscinet  zmath  isi  elib  scopus
    3. P. Acosta-Humanez, H. Giraldo, C. Piedrahita, “Differential Galois groups and representation of quivers for seismic models with constant Hessian of square of slowness”, Far East Journal of Mathematical Sciences, 102:3 (2017), 599-623  crossref  zmath  scopus
    4. Manuel F. Acosta-Humánez, Primitivo B. Acosta-Humánez, Erick Tuirán, “Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory”, SIGMA, 14 (2018), 099, 21 pp.  mathnet  crossref
    5. Acosta-Humanez P.B., Reyes-Linero A., Rodriguez-Contreras J., “Galoisian and Qualitative Approaches to Linear Polyanin-Zaitsev Vector Fields”, Open Math., 16 (2018), 1204–1217  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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