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

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

1999-12-06

arxiv.org/abs/solv-int/9912005v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, LaTeX, talk at "Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives" (August 1999, Chern

Scientific paper

Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius 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 B\"acklund transformation. A more general class of multicomponent M\"obius-type symmetries is studied. It is demonstrated that symmetry constraints of KP hierarchy defined using multicomponent M\"obius-type symmetries give rise to Calogero-Moser system.

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