Integrable Hierarchy of the Quantum Benjamin-Ono Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Maxim Nazarov¹  Evgeny Sklyanin¹ 

[1] Department of Mathematics, University of York, United Kingdom

关键词: Jack symmetric functions;    quantum Benjamin–Ono equation;    collective variables;   

DOI  :  10.3842/SIGMA.2013.078

来源: National Academy of Science of Ukraine

【 摘 要 】

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

【 授权许可】

Unknown