Classification of Multidimensional Darboux Transformations: First Order and Continued Type
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations o...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148605 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Classification of Multidimensional Darboux Transformations: First Order and Continued Type / D. Hobby, E. Shemyakova // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 40 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862592548584816640 |
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| author | Hobby, D. Shemyakova, E. |
| author_facet | Hobby, D. Shemyakova, E. |
| citation_txt | Classification of Multidimensional Darboux Transformations: First Order and Continued Type / D. Hobby, E. Shemyakova // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 40 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a complete description of all possible first-order Darboux transformations. We introduce a large class of invertible Darboux transformations of higher order, which we call Darboux transformations of continued Type I. This generalizes the class of Darboux transformations of Type I, which was previously introduced. There is also a modification of this type of Darboux transformations, continued Wronskian type, which generalize Wronskian type Darboux transformations.
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| first_indexed | 2025-11-27T08:40:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148605 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T08:40:09Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hobby, D. Shemyakova, E. 2019-02-18T16:30:31Z 2019-02-18T16:30:31Z 2017 Classification of Multidimensional Darboux Transformations: First Order and Continued Type / D. Hobby, E. Shemyakova // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16S32; 37K35; 37K25 DOI:10.3842/SIGMA.2017.010 https://nasplib.isofts.kiev.ua/handle/123456789/148605 We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a complete description of all possible first-order Darboux transformations. We introduce a large class of invertible Darboux transformations of higher order, which we call Darboux transformations of continued Type I. This generalizes the class of Darboux transformations of Type I, which was previously introduced. There is also a modification of this type of Darboux transformations, continued Wronskian type, which generalize Wronskian type Darboux transformations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Classification of Multidimensional Darboux Transformations: First Order and Continued Type Article published earlier |
| spellingShingle | Classification of Multidimensional Darboux Transformations: First Order and Continued Type Hobby, D. Shemyakova, E. |
| title | Classification of Multidimensional Darboux Transformations: First Order and Continued Type |
| title_full | Classification of Multidimensional Darboux Transformations: First Order and Continued Type |
| title_fullStr | Classification of Multidimensional Darboux Transformations: First Order and Continued Type |
| title_full_unstemmed | Classification of Multidimensional Darboux Transformations: First Order and Continued Type |
| title_short | Classification of Multidimensional Darboux Transformations: First Order and Continued Type |
| title_sort | classification of multidimensional darboux transformations: first order and continued type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148605 |
| work_keys_str_mv | AT hobbyd classificationofmultidimensionaldarbouxtransformationsfirstorderandcontinuedtype AT shemyakovae classificationofmultidimensionaldarbouxtransformationsfirstorderandcontinuedtype |