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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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147157 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1471572019-02-14T01:25:25Z Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity Kasman, A. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147157 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 |
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. |
| format |
Article |
| author |
Kasman, A. |
| spellingShingle |
Kasman, A. Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kasman, A. |
| author_sort |
Kasman, A. |
| title |
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kasmana bispectralityofncomponentkpwavefunctionsastudyinnoncommutativity |
| first_indexed |
2023-05-20T17:26:44Z |
| last_indexed |
2023-05-20T17:26:44Z |
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1796153311611584512 |