KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–

A series of new hierarchies of soliton equations are presented on the basis of the Kadomtsev-Petviashvili (KP) hierarchy. In contrast to the KP case, which admits GL( ∞) as its transformation group, these new hierarchies are shown to correspond to O( ∞) or Sp( ∞). Soliton, rational and quasi-periodic solutions are constructed.