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 . This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849, arXiv:1212.2781].
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}
}