Integrable Hierarchy of the Quantum Benjamin-Ono Equation

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,…. 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].