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SIGMA, 2012, Volume 8, 069, 10 pages (Mi sigma746)  

This article is cited in 13 scientific papers (total in 13 papers)

Complex SUSY transformations and the Painlevé IV equation

David Bermúdez

Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico

Abstract: In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlevé IV equation with complex parameters. We present some concrete examples of such solutions.

Keywords: supersymmetric quantum mechanics; Painlevé equations; differential equations; quantum harmonic oscillator; polynomial Heisenberg algebras.

DOI: https://doi.org/10.3842/SIGMA.2012.069

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Full text: http://emis.mi.ras.ru/.../069
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Bibliographic databases:

ArXiv: 1208.1782
MSC: 81Q60; 35G20; 34M55
Received: July 29, 2012; in final form September 28, 2012; Published online October 11, 2012
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Citation: David Bermúdez, “Complex SUSY transformations and the Painlevé IV equation”, SIGMA, 8 (2012), 069, 10 pp.

Citation in format AMSBIB
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\by David Berm\'udez
\paper Complex SUSY transformations and the Painlev\'e IV equation
\jour SIGMA
\yr 2012
\vol 8
\papernumber 069
\totalpages 10
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Iyela D.B. Govaerts J. Hounkonnou M.N., “Supersymmetric Quantum Mechanics: Engineered Hierarchies of Integrable Potentials and Related Orthogonal Polynomials”, J. Math. Phys., 54:9 (2013), 093502  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Fernandez D.J. Morales-Salgado V.S., “Supersymmetric Partners of the Harmonic Oscillator with an Infinite Potential Barrier”, J. Phys. A-Math. Theor., 47:3 (2014), 035304  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Bermudez D., Fernandez C D.J., “Supersymmetric Quantum Mechanics and Painlevé Equations”, Latin-American School of Physics Marcos Moshinsky Elaf: Nonlinear Dynamics in Hamiltonian Systems, AIP Conference Proceedings, 1575, eds. Bijker R., Castanos O., Jauregui R., Lemus R., RosasOrtiz O., Amer Inst Physics, 2014, 50–88  crossref  isi  scopus
    4. Fernandez C D.J. Morales-Salgado V.S., “Supersymmetric Partners of the Truncated Harmonic Oscillator”, 8th International Symposium on Quantum Theory and Symmetries, Journal of Physics Conference Series, 512, IOP Publishing Ltd, 2014, 012024  crossref  isi  scopus
    5. Fernandez C. David J. Gonzalez J.C., “Complex Oscillator and Painlevé Iv Equation”, Ann. Phys., 359 (2015), 213–229  crossref  mathscinet  zmath  isi  scopus
    6. Bermudez D. Fernandez C D.J., “a Connection Between Supersymmetric Quantum Mechanics and Painlevé V Equation”, International Conference on Quantum Control, Exact Or Perturbative, Linear Or Nonlinear To Celebrate 50 Years of the Scientific Career of Professor Bogdan Mielnik, Journal of Physics Conference Series, 624, ed. Breton N. Fernandez D. Kielanowski P., IOP Publishing Ltd, 2015, 012012  crossref  isi  scopus
    7. Fernandez C D.J. Morales-Salgado V.S., “Truncated Harmonic Oscillator and Painlevé Iv and V Equations”, International Conference on Quantum Control, Exact Or Perturbative, Linear Or Nonlinear To Celebrate 50 Years of the Scientific Career of Professor Bogdan Mielnik, Journal of Physics Conference Series, 624, ed. Breton N. Fernandez D. Kielanowski P., IOP Publishing Ltd, 2015, 012017  crossref  isi  scopus
    8. Fernandez C D.J. Gonzalez J.C., “Susy Partners of the Complex Oscillator and Painlevé Iv Equation”, International Conference on Quantum Control, Exact Or Perturbative, Linear Or Nonlinear To Celebrate 50 Years of the Scientific Career of Professor Bogdan Mielnik, Journal of Physics Conference Series, 624, ed. Breton N. Fernandez D. Kielanowski P., IOP Publishing Ltd, 2015, 012015  crossref  isi  scopus
    9. Fernandez C D.J. Morales-Salgado V.S., “Factorization Method For the Truncated Harmonic Oscillator”, XXXth International Colloquium on Group Theoretical Methods in Physics, Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012035  crossref  isi  scopus
    10. Bermudez D., Fernandez C D.J., Negro J., “Solutions to the Painlevé V equation through supersymmetric quantum mechanics”, J. Phys. A-Math. Theor., 49:33 (2016), 335203  crossref  mathscinet  zmath  isi  elib  scopus
    11. Fernandez C D.J., Morales-Salgado V.S., “SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations”, J. Phys. A-Math. Theor., 49:19 (2016), 195202  crossref  mathscinet  zmath  isi  elib  scopus
    12. Fernandez D.J.C., “Painlevé equations and supersymmetric quantum mechanics”, Geometric Methods in Physics, Trends in Mathematics, eds. Kielanowski P., Ali S., Bieliavsky P., Odzijewicz A., Schlichenmaier M., Voronov T., Springer Int Publishing Ag, 2016, 213–231  crossref  mathscinet  zmath  isi
    13. Rogers C., Bassom A.P., Clarkson P.A., “On Integrable Ermakov-Painlevé Iv Systems”, J. Math. Anal. Appl., 462:2 (2018), 1225–1241  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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