Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser System
Abstract
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.