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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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Main Authors:	Hobby, D., Shemyakova, E.
Format:	Article
Language:	English
Published:	Інститут математики НАН України 2017
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Online Access:	http://dspace.nbuv.gov.ua/handle/123456789/148605
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id	irk-123456789-148605
record_format	dspace
spelling	irk-123456789-1486052019-02-19T01:25:53Z Classification of Multidimensional Darboux Transformations: First Order and Continued Type Hobby, D. Shemyakova, E. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148605 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
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.
format	Article
author	Hobby, D. Shemyakova, E.
spellingShingle	Hobby, D. Shemyakova, E. Classification of Multidimensional Darboux Transformations: First Order and Continued Type Symmetry, Integrability and Geometry: Methods and Applications
author_facet	Hobby, D. Shemyakova, E.
author_sort	Hobby, D.
title	Classification of Multidimensional Darboux Transformations: First Order and Continued Type
title_short	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_sort	classification of multidimensional darboux transformations: first order and continued type
publisher	Інститут математики НАН України
publishDate	2017
url	http://dspace.nbuv.gov.ua/handle/123456789/148605
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.
series	Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv	AT hobbyd classificationofmultidimensionaldarbouxtransformationsfirstorderandcontinuedtype AT shemyakovae classificationofmultidimensionaldarbouxtransformationsfirstorderandcontinuedtype
first_indexed	2023-05-20T17:29:45Z
last_indexed	2023-05-20T17:29:45Z
_version_	1796153423003910144

Classification of Multidimensional Darboux Transformations: First Order and Continued Type

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