منابع مشابه
Painlev e-Calogero correspondence
The so called “Painlevé-Calogero correspondence” relates the sixth Painlevé equation with an integrable system of the Calogero type. This relation was recently generaized to the other Painlevé equations and a “multi-component” analogue. This paper reviews these results. 1 Historical background It was at the beginning of the twentieth century that Painlevé discovered what are nowadays called the...
متن کاملPainlevé-Calogero Correspondence Revisited
We extend the work of Fuchs, Painlevé and Manin on a Calogero-like expression of the sixth Painlevé equation (the “Painlevé-Calogero correspondence”) to the other five Painlevé equations. The Calogero side of the sixth Painlevé equation is known to be a non-autonomous version of the (rank one) elliptic model of Inozemtsev’s extended Calogero systems. The fifth and fourth Painlevé equations corr...
متن کاملCorrespondence between conformal field theory and Calogero - Sutherland model
We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators Ln. We calculate explicitly the matrix elements of Ln with respect to the Jack-basis. A combinatorial procedure which produces these matrix elements is conjectured. As a limiting case of the formula, we obtain a Pieri-type formula which represents a product of a power sum and a Jack...
متن کاملElliptic Linear Problem for Calogero - Inozemtsev Model and Painlevé VI Equation
We introduce 3N × 3N Lax pair with spectral parameter for Calogero-Inozemtsev model. The one degree of freedom case appears to have 2 × 2 Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides elliptic linear problem for the Painlevé VI equation in elliptic form.
متن کاملQuantum Solitons in the Calogero-Sutherland Model
We show that the single quasi-particle Schrödinger equation for a certain form of one-body potential yields a stationary one soliton solution. The one-body potential is assumed to arise from the self-interacting charge distribution with the singular kernel of the Calogero-Sutherland model. The quasi-particle has negative or positive charge for negative or positive coupling constant of the inter...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2012
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4732532