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Integrable Hierarchy of the Quantum Benjamin-Ono Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Integrable Hierarchy of the Quantum Benjamin-Ono Equation
Інший ID:
2010 Mathematics Subject Classification: 33D52; 05E05; 37K10; 81Q80
DOI: http://dx.doi.org/10.3842/SIGMA.2013.078
DOI: http://dx.doi.org/10.3842/SIGMA.2013.078
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
503
Завантажень:
219
Анотація:
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].
