Complex SUSY Transformations and the Painlevé IV Equation
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148467 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Complex SUSY Transformations and the Painlevé IV Equation / D. Bermúdez // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862536049622777856 |
|---|---|
| author | Bermúdez, D. |
| author_facet | Bermúdez, D. |
| citation_txt | Complex SUSY Transformations and the Painlevé IV Equation / D. Bermúdez // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-24T11:04:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148467 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T11:04:32Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bermúdez, D. 2019-02-18T13:25:45Z 2019-02-18T13:25:45Z 2012 Complex SUSY Transformations and the Painlevé IV Equation / D. Bermúdez // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60; 35G20; 34M55 DOI: http://dx.doi.org/10.3842/SIGMA.2012.069 https://nasplib.isofts.kiev.ua/handle/123456789/148467 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. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html.
 The author would like to acknowledge the useful comments of Professor David J. Fern´andez C. and his revision of the manuscript. The author also acknowledges the support of Conacyt (Mexico) through the PhD scholarship 219665 and the project 152574. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Complex SUSY Transformations and the Painlevé IV Equation Article published earlier |
| spellingShingle | Complex SUSY Transformations and the Painlevé IV Equation Bermúdez, D. |
| title | Complex SUSY Transformations and the Painlevé IV Equation |
| title_full | Complex SUSY Transformations and the Painlevé IV Equation |
| title_fullStr | Complex SUSY Transformations and the Painlevé IV Equation |
| title_full_unstemmed | Complex SUSY Transformations and the Painlevé IV Equation |
| title_short | Complex SUSY Transformations and the Painlevé IV Equation |
| title_sort | complex susy transformations and the painlevé iv equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148467 |
| work_keys_str_mv | AT bermudezd complexsusytransformationsandthepainleveivequation |