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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149370 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862717217729150976 |
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| author | Nazarov, M. Sklyanin, E. |
| author_facet | Nazarov, M. Sklyanin, E. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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].
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| first_indexed | 2025-12-07T18:09:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149370 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:09:21Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Integrable Hierarchy of the Quantum Benjamin-Ono Equation Nazarov, M. Sklyanin, E. |
| title | 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_short | Integrable Hierarchy of the Quantum Benjamin-Ono Equation |
| title_sort | integrable hierarchy of the quantum benjamin-ono equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149370 |
| work_keys_str_mv | AT nazarovm integrablehierarchyofthequantumbenjaminonoequation AT sklyanine integrablehierarchyofthequantumbenjaminonoequation |