Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
We construct rational extensions of the Darboux-Pöschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only quasi-isospectral. Both are associated to new families of orthogonal polynom...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147132 |
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| Zitieren: | Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials / Y. Grandati, C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. |
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Grandati, Y. Quesne, C. 2019-02-13T17:17:58Z 2019-02-13T17:17:58Z 2015 Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials / Y. Grandati, C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q05; 81Q60; 42C05 DOI:10.3842/SIGMA.2015.061 https://nasplib.isofts.kiev.ua/handle/123456789/147132 We construct rational extensions of the Darboux-Pöschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only quasi-isospectral. Both are associated to new families of orthogonal polynomials, which, in the first case, depend on a continuous parameter. We also prove that these extended potentials possess an enlarged shape invariance property. This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials |
| spellingShingle |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials Grandati, Y. Quesne, C. |
| title_short |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials |
| title_full |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials |
| title_fullStr |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials |
| title_full_unstemmed |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials |
| title_sort |
confluent chains of dbt: enlarged shape invariance and new orthogonal polynomials |
| author |
Grandati, Y. Quesne, C. |
| author_facet |
Grandati, Y. Quesne, C. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We construct rational extensions of the Darboux-Pöschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only quasi-isospectral. Both are associated to new families of orthogonal polynomials, which, in the first case, depend on a continuous parameter. We also prove that these extended potentials possess an enlarged shape invariance property.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147132 |
| citation_txt |
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials / Y. Grandati, C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. |
| work_keys_str_mv |
AT grandatiy confluentchainsofdbtenlargedshapeinvarianceandneworthogonalpolynomials AT quesnec confluentchainsofdbtenlargedshapeinvarianceandneworthogonalpolynomials |
| first_indexed |
2025-11-27T10:33:03Z |
| last_indexed |
2025-11-27T10:33:03Z |
| _version_ |
1850852099282173952 |