A Reciprocal Transformation for the Constant Astigmatism Equation
We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation zyy+(1/z)xx+2=0. The transformation is related to the special case of the famous Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter λ=±1. It is also a nonlocal symmetr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146605 |
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| Zitieren: | A Reciprocal Transformation for the Constant Astigmatism Equation / A. Hlaváč, M. Marvan // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 31 назв. — англ. |
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Hlaváč, A. Marvan, M. 2019-02-10T09:55:00Z 2019-02-10T09:55:00Z 2014 A Reciprocal Transformation for the Constant Astigmatism Equation / A. Hlaváč, M. Marvan // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A05; 35A30; 35C05; 37K35 DOI:10.3842/SIGMA.2014.091 https://nasplib.isofts.kiev.ua/handle/123456789/146605 We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation zyy+(1/z)xx+2=0. The transformation is related to the special case of the famous Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter λ=±1. It is also a nonlocal symmetry. We are indebted to I.S. Krasil’shchik for reading the manuscript and valuable comments. A.H. was supported by Silesian University in Opava under the student grant project SGS/1/2011, M.M. was supported by GACR under project P201/11/0356. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Reciprocal Transformation for the Constant Astigmatism Equation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Reciprocal Transformation for the Constant Astigmatism Equation |
| spellingShingle |
A Reciprocal Transformation for the Constant Astigmatism Equation Hlaváč, A. Marvan, M. |
| title_short |
A Reciprocal Transformation for the Constant Astigmatism Equation |
| title_full |
A Reciprocal Transformation for the Constant Astigmatism Equation |
| title_fullStr |
A Reciprocal Transformation for the Constant Astigmatism Equation |
| title_full_unstemmed |
A Reciprocal Transformation for the Constant Astigmatism Equation |
| title_sort |
reciprocal transformation for the constant astigmatism equation |
| author |
Hlaváč, A. Marvan, M. |
| author_facet |
Hlaváč, A. Marvan, M. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation zyy+(1/z)xx+2=0. The transformation is related to the special case of the famous Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter λ=±1. It is also a nonlocal symmetry.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146605 |
| citation_txt |
A Reciprocal Transformation for the Constant Astigmatism Equation / A. Hlaváč, M. Marvan // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 31 назв. — англ. |
| work_keys_str_mv |
AT hlavaca areciprocaltransformationfortheconstantastigmatismequation AT marvanm areciprocaltransformationfortheconstantastigmatismequation AT hlavaca reciprocaltransformationfortheconstantastigmatismequation AT marvanm reciprocaltransformationfortheconstantastigmatismequation |
| first_indexed |
2025-12-07T13:30:23Z |
| last_indexed |
2025-12-07T13:30:23Z |
| _version_ |
1850856411719794688 |