English

Integrable Hierarchy of the Quantum Benjamin-Ono Equation

Exactly Solvable and Integrable Systems 2017-03-10 v2 Combinatorics Representation Theory

Abstract

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,x_1,x_2,\ldots. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions pn=x1n+x2n+p_n=x_1^n+x_2^n+\cdots and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849, arXiv:1212.2781].

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Cite

@article{arxiv.1309.6464,
  title  = {Integrable Hierarchy of the Quantum Benjamin-Ono Equation},
  author = {Maxim Nazarov and Evgeny Sklyanin},
  journal= {arXiv preprint arXiv:1309.6464},
  year   = {2017}
}
R2 v1 2026-06-22T01:33:41.877Z