Invertible Darboux Transformations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Invertible Darboux Transformations
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| Creator |
Shemyakova, E.
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| 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.
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| Date |
2019-02-19T18:29:49Z
2019-02-19T18:29:49Z 2013 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/149197 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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