Integrable hierarchy of the quantum Benjamin-Ono equation

TY - JOUR

T1 - Integrable hierarchy of the quantum Benjamin-Ono equation

AU - Nazarov, Maxim L

AU - Sklyanin, Evgeny

PY - 2013/12/7

Y1 - 2013/12/7

N2 - 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 of those variables and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849].

AB - 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 of those variables and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849].

KW - Jack symmetric functions

KW - Quantum Benjamin-Ono equation

KW - Collective variables

UR - https://arxiv.org/abs/1309.6464

U2 - 10.3842/SIGMA.2013.078

DO - 10.3842/SIGMA.2013.078

M3 - Article

SN - 1815-0659

VL - 9

JO - Symmetry integrability and geometry-Methods and applications

JF - Symmetry integrability and geometry-Methods and applications

M1 - 078

ER -