Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy
نویسنده
چکیده
Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser system.
منابع مشابه
Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser System
Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that Möbius symmetry transformation for the singular manifold equation leads to continuous or discrete non-isospectral symmetry of the basic (scalar or multicomponent KP) hierarchy connected with binary Bäcklund transformation. A more general class of multi...
متن کاملKP Trigonometric Solitons and an Adelic Flag Manifold
We show that the trigonometric solitons of the KP hierarchy enjoy a differentialdifference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wilson’s fundamental idea [Invent. Math. 133 (1998), 1–41] for understanding the (self-dual) bispectr...
متن کاملar X iv : m at h / 03 10 49 0 v 1 [ m at h . A G ] 3 1 O ct 2 00 3 FROM SOLITONS TO MANY – BODY SYSTEMS
We present a bridge between the KP soliton equations and the Calogero–Moser many-body systems through noncommutative algebraic geometry. The Calogero-Moser systems have a natural geometric interpretation as flows on spaces of spectral curves on a ruled surface. We explain how the meromorphic solutions of the KP hierarchy have an interpretation via a noncommutative ruled surface. Namely, we iden...
متن کاملCalogero-Moser hierarchy and KP hierarchy
In [1], Airault, McKean and Moser observed that the motion of poles of a rational solution to the K-dV or Boussinesq equation obeys the Calogero-Moser dynamical system [2, 3, 4] with an extra condition on the configuration of poles. In [8], Krichever observed that the motion of poles of a solution to the KP equation which is rational in t1 obeys the Calogero-Moser dynamical system. In this note...
متن کاملSpin Calogero Particles and Bispectral Solutions of the Matrix Kp Hierarchy
Pairs of n×n matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with r × r matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the...
متن کامل