Algebraic internal wave solitons and the integrable Calogero–Moser–Sutherland <i>N</i>-body problem

Chen, H. H.; Lee, Y. C.; Pereira, N. R.

doi:10.1063/1.862457

Cited by 98 publications

(72 citation statements)

References 15 publications

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“…The latter is a minor generalization of the conventional Benjamin-Ono equation (BO) arising in the hydrodynamics of stratified fluids [7]. A connection of the traditional BO to a complexified version of a classical Calogero model is known [8]. A pair of coupled classical BO-type equations has been obtained by A. Jevicki for a long-wave description of free fermions (λ = 1) [4].…”

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confidence: 99%

Quantum Hydrodynamics, the Quantum Benjamin-Ono Equation, and the Calogero Model

2005

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Collective field theory for Calogero model represents particles with fractional statistics in terms of hydrodynamic modes -density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field -quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.

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confidence: 99%

Quantum Hydrodynamics, the Quantum Benjamin-Ono Equation, and the Calogero Model

2005

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“…The contribution of this image to the b velocity parallels the interaction of a b and a = b * pair in the original real-valued Benjamin-Ono equation studied in [15]-the only difference being that in the present case we must include inḃ the constant velocity v sound = λπρ 0 induced by the uniform ρ 0 background. The condition thatȧ(0) be real is a linear equation linking the b-pole contribution to the density fluctuation δρ = (ρ − ρ 0 ).…”

Section: Shepherd Poles and Calogero Density-wave Solitonsmentioning

confidence: 81%

“…This Hamiltonian system possesses infinitely many Poisson-commuting integrals of motion [14]. Following [15], we seek solutions of (1) as a sum of poles…”

Section: Calogero-sutherland From the Benjamin-ono Pole Ansatzmentioning

confidence: 99%

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Characteristics of the Flow of an Incompressible Fluid in a Gravitational Field

Fedoryuk¹

1990

Math. USSR Sb.

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We explore the classical version of the mapping, due to Abanov and Wiegmann, of Calogero-Sutherland hydrodynamics onto the Benjamin-Ono equation 'on the double'. We illustrate the mapping by constructing the soliton solutions to the hydrodynamic equations, and show how certain subtleties arise from the need to include corrections to the naïve replacement of singular sums by principal-part integrals.

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“…Thus, assuming θ ε has been constructed from the constraints (i)-(v), we may obtain θ ε by solving the equations 35) involving the standard inner product. This means (θ ε ) −1 α i = (θ ε α) i .…”

Section: (C) Deformed Calogero-moser-sutherland Modelsmentioning

confidence: 99%

PT -symmetric deformations of integrable models

Fring

2013

Phil. Trans. R. Soc. A.

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We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and non-linear integrable field equations of Korteweg-de-Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models we provide three alternative deformations: A complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real valued field equations of non linear integrable systems and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of KdV-type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.Comment: 21 pages, 3 figure

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Algebraic internal wave solitons and the integrable Calogero–Moser–Sutherland N-body problem

Abstract: The Benjamin–Ono equation that describes nonlinear internal waves in a stratified fluid is solved by a pole expansion method. The dynamics of poles which characterize solitons is shown to be identical to the well-known integrable N-body problem of Calogero, Moser, and Sutherland.

Cited by 98 publications

References 15 publications

Quantum Hydrodynamics, the Quantum Benjamin-Ono Equation, and the Calogero Model

Quantum Hydrodynamics, the Quantum Benjamin-Ono Equation, and the Calogero Model

Characteristics of the Flow of an Incompressible Fluid in a Gravitational Field

PT -symmetric deformations of integrable models

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