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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 069, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.069 (Mi sigma746) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Complex SUSY transformations and the Painlevé IV equation

David Bermúdez

Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico
Full-text PDF (508 kB) Citations (15)
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DOI: https://doi.org/10.3842/SIGMA.2012.069
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.
Received: July 29, 2012; in final form September 28, 2012; Published online October 11, 2012
Bibliographic databases:
Document Type: Article
MSC: 81Q60; 35G20; 34M55
Language: English
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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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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