Invertible Darboux Transformations
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149197 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Invertible Darboux Transformations / E. Shemyakova // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862752334801534976 |
|---|---|
| author | Shemyakova, E. |
| author_facet | Shemyakova, E. |
| citation_txt | Invertible Darboux Transformations / E. Shemyakova // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases of Darboux transformations for hyperbolic bivariate operators of order 2. In the present paper we find a criteria for a bivariate linear partial differential operator of an arbitrary order d to have an invertible Darboux transformation. We show that Wronkian formulae may fail in some cases, and find sufficient conditions for such formulae to work.
|
| first_indexed | 2025-12-07T21:16:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149197 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:16:26Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Shemyakova, E. 2019-02-19T18:29:49Z 2019-02-19T18:29:49Z 2013 Invertible Darboux Transformations / E. Shemyakova // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 37K15 DOI: http://dx.doi.org/10.3842/SIGMA.2013.002 https://nasplib.isofts.kiev.ua/handle/123456789/149197 For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases of Darboux transformations for hyperbolic bivariate operators of order 2. In the present paper we find a criteria for a bivariate linear partial differential operator of an arbitrary order d to have an invertible Darboux transformation. We show that Wronkian formulae may fail in some cases, and find sufficient conditions for such formulae to work. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Invertible Darboux Transformations Article published earlier |
| spellingShingle | Invertible Darboux Transformations Shemyakova, E. |
| title | Invertible Darboux Transformations |
| title_full | Invertible Darboux Transformations |
| title_fullStr | Invertible Darboux Transformations |
| title_full_unstemmed | Invertible Darboux Transformations |
| title_short | Invertible Darboux Transformations |
| title_sort | invertible darboux transformations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149197 |
| work_keys_str_mv | AT shemyakovae invertibledarbouxtransformations |