R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence

Abstract

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.

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

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• On Two-Current Realization of KP Hierarchy
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• Constrained KP Models as Integrable Matrix Hierarchies
• Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies
• Construction of KP Hierarchies in Terms of Finite Number of Fields and their Abelianization
• Affine Lie Algebraic Origin of Constrained KP Hierarchies
• Manifestly Supersymmetric Lax Integrable Hierarchies
• On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy
• Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System
• On Discrete Symmetries of the Multi-Boson KP Hierarchies
• Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy
• Hamiltonian Structures of the Multi-Boson KP Hierarchies, Abelianization and Lattice Formulation
• Compatible Poisson Structures of Toda Type Discrete Hierarchy
• Generalized Riemann-Hilbert-Birkhoff Decomposition and a New Class of Higher Grading Integrable Hierarchies
• On Non-Linear W-Infinity Symmetry of Generalized Liouville and Conformal Toda Models
• Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems