R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence

Details R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence

1992-09-01

arxiv.org/abs/hep-th/9209006v1

Phys.Lett. B294 (1992) 167-176

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, Latex, CERN-TH.6627/92

Scientific paper

10.1016/0370-2693(92)90678-W

The Adler-Kostant-Symes $R$-bracket scheme is applied to the algebra of pseudo-differential operators to relate the three integrable hierarchies: KP and its two modifications, known as nonstandard integrable models. All three hierarchies are shown to be equivalent and connection is established in the form of a symplectic gauge transformation. This construction results in a new representation of the W-infinity algebras in terms of 4 bosonic fields.

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