Integrable Hierarchy of the Quantum Benjamin-Ono Equation
A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x₁,x₂,…. This construction provides explicit expressions for the Hami...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149370 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Integrable Hierarchy of the Quantum Benjamin-Ono Equation / M. Nazarov, E. Sklyanin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149370 |
|---|---|
| record_format |
dspace |
| spelling |
Nazarov, M. Sklyanin, E. 2019-02-21T07:26:23Z 2019-02-21T07:26:23Z 2013 Integrable Hierarchy of the Quantum Benjamin-Ono Equation / M. Nazarov, E. Sklyanin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D52; 05E05; 37K10; 81Q80 DOI: http://dx.doi.org/10.3842/SIGMA.2013.078 https://nasplib.isofts.kiev.ua/handle/123456789/149370 A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x₁,x₂,…. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions pn=x₁ⁿ+x₂ⁿ+⋯ and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849]. This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html. We are very grateful to S.M. Khoroshkin and J. Shiraishi for friendly discussions. We cannot praise enough the wonderful Maple packages by J. Stembridge [17] that facilitated our work with symmetric functions. The first and the second named of us have been supported by the EPSRC grants EP/I014071 and EP/H000054 respectively. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrable Hierarchy of the Quantum Benjamin-Ono Equation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation |
| spellingShingle |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation Nazarov, M. Sklyanin, E. |
| title_short |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation |
| title_full |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation |
| title_fullStr |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation |
| title_full_unstemmed |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation |
| title_sort |
integrable hierarchy of the quantum benjamin-ono equation |
| author |
Nazarov, M. Sklyanin, E. |
| author_facet |
Nazarov, M. Sklyanin, E. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x₁,x₂,…. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions pn=x₁ⁿ+x₂ⁿ+⋯ and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849].
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149370 |
| citation_txt |
Integrable Hierarchy of the Quantum Benjamin-Ono Equation / M. Nazarov, E. Sklyanin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. |
| work_keys_str_mv |
AT nazarovm integrablehierarchyofthequantumbenjaminonoequation AT sklyanine integrablehierarchyofthequantumbenjaminonoequation |
| first_indexed |
2025-12-07T18:09:21Z |
| last_indexed |
2025-12-07T18:09:21Z |
| _version_ |
1850873963020812288 |