Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser System
نویسنده
چکیده
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 multicomponent Möbius-type symmetries is studied. It is demonstrated that symmetry constraints of KP hierarchy defined using multicomponent Möbius-type symmetries give rise to Calogero-Moser system.
منابع مشابه
Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy
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.
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 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 کاملSquared Eigenfunctions of the (modiied) Kp Hierarchy and Scattering Problems of Loewner Type
It is shown that products of eigenfunctions and (integrated) adjoint eigenfunctions associated with the (modiied) Kadomtsev-Petviashvili (KP) hierarchy form generators of a symmetry transformation. Linear integro-diierential representations for these symmetries are found. For special cases the corresponding nonlinear equations are the compatibility conditions of linear scattering problems of Lo...
متن کاملHidden symmetry of the quantum Calogero-Moser system
Hidden symmetry of the quantum Calogero-Moser system with the inverse-square potential is explicitly demonstrated in algebraic sense. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel functions are also discussed.
متن کامل