KP hierarchies of orthogonal and symplectic type. Transformation groups for soliton equations. VI.(English)Zbl 0571.35102

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 $${\mathfrak gl}(\infty)$$ as its transformation group, these new hierarchies are shown to correspond to o($$\infty)$$ or $${\mathfrak sp}(\infty)$$. Soliton, rational and quasi-periodic solutions are constructed.

MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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