2013
DOI: 10.3842/sigma.2013.078
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Integrable Hierarchy of the Quantum Benjamin-Ono Equation

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Cited by 32 publications
(130 citation statements)
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“…In § [6] we present the Hamiltonian and Lax operator of a preliminary geometric quantization of (1.1). In § [7] we show how a modification of our preliminary quantization by the renormalization (1.9) of Abanov-Wiegmann [1] is implicit in the solution of the quantization problem for (1.1) by Nazarov-Sklyanin [40]. In § [8] we present the exact spectrum of the quantum periodic Benjamin-Ono hierarchy from [40].…”
Section: Figmentioning
confidence: 96%
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“…In § [6] we present the Hamiltonian and Lax operator of a preliminary geometric quantization of (1.1). In § [7] we show how a modification of our preliminary quantization by the renormalization (1.9) of Abanov-Wiegmann [1] is implicit in the solution of the quantization problem for (1.1) by Nazarov-Sklyanin [40]. In § [8] we present the exact spectrum of the quantum periodic Benjamin-Ono hierarchy from [40].…”
Section: Figmentioning
confidence: 96%
“…As will appear in [37], Theorem [1.3.1] implies that the semi-classical and small dispersion asymptotics in the author's thesis [38] on Jack measures, a generalization of Okounkov's Schur measures [45], reflect the structure of quantum dispersive shock waves and quantum soliton trains emitted by coherent states from [5]. Note that a classical version of these small dispersion asymptotics, relating dispersive action profiles of the classical hierarchy in [40] to the formation of classical dispersive shock waves, has already been given by the author in [39]. 1.6.…”
Section: Figmentioning
confidence: 99%
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“…Such quantum integrable hierarchies exist e.g. for the quantum KdV system [35] and the quantum Benjamin-Ono equation [36].…”
Section: Local Spin Chainsmentioning
confidence: 99%