Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity
A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix differential operat...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147157 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity / A. Kasman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147157 |
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Kasman, A. 2019-02-13T17:50:53Z 2019-02-13T17:50:53Z 2015 Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity / A. Kasman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34L05; 16S32; 37K10 DOI:10.3842/SIGMA.2015.087 https://nasplib.isofts.kiev.ua/handle/123456789/147157 A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix differential operators in x having eigenvalues that are matrix functions of the spectral parameter z. If the space of distributions is invariant under left multiplication by H, then a matrix coefficient differential-translation operator in z is shown to share this eigenfunction and have an eigenvalue that is a matrix function of x. This paper not only generates new examples of bispectral operators, it also explores the consequences of non-commutativity for techniques and objects used in previous investigations. The author thanks the College of Charleston for the sabbatical during which this work was completed, Maarten Bergvelt and Michael Gekhtman for mathematical assistance as well as serving as gracious hosts, Chunxia Li for carefully reading and commenting on early drafts, and the referees for their advices. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity |
| spellingShingle |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity Kasman, A. |
| title_short |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity |
| title_full |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity |
| title_fullStr |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity |
| title_full_unstemmed |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity |
| title_sort |
bispectrality of n-component kp wave functions: a study in non-commutativity |
| author |
Kasman, A. |
| author_facet |
Kasman, A. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix differential operators in x having eigenvalues that are matrix functions of the spectral parameter z. If the space of distributions is invariant under left multiplication by H, then a matrix coefficient differential-translation operator in z is shown to share this eigenfunction and have an eigenvalue that is a matrix function of x. This paper not only generates new examples of bispectral operators, it also explores the consequences of non-commutativity for techniques and objects used in previous investigations.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147157 |
| citation_txt |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity / A. Kasman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 33 назв. — англ. |
| work_keys_str_mv |
AT kasmana bispectralityofncomponentkpwavefunctionsastudyinnoncommutativity |
| first_indexed |
2025-11-27T14:28:45Z |
| last_indexed |
2025-11-27T14:28:45Z |
| _version_ |
1850852478925406208 |