R-matrix formulation of KP hierarchies and their gauge equivalence

Abstract The Adler-Kostant-Symes R -bracket scheme is applied to the algebra of pseudodifferential operators to relate the three integrable hierarchies: KP and its two modifications, known as non-standard integrable models. All three hierarchies are shown to be equivalent and a 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 four boson fields.