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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146605 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862623839248187392 |
|---|---|
| author | Hlaváč, A. Marvan, M. |
| author_facet | Hlaváč, A. Marvan, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T13:30:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146605 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:30:23Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | A Reciprocal Transformation for the Constant Astigmatism Equation Hlaváč, A. Marvan, M. |
| title | 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_short | A Reciprocal Transformation for the Constant Astigmatism Equation |
| title_sort | reciprocal transformation for the constant astigmatism equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146605 |
| work_keys_str_mv | AT hlavaca areciprocaltransformationfortheconstantastigmatismequation AT marvanm areciprocaltransformationfortheconstantastigmatismequation AT hlavaca reciprocaltransformationfortheconstantastigmatismequation AT marvanm reciprocaltransformationfortheconstantastigmatismequation |