On Two-Current Realization of KP Hierarchy

Abstract

A simple description of the KP hierarchy and its multi-hamiltonian structure is given in terms of two Bose currents. A deformation scheme connecting various W-infinity algebras and relation between two fundamental nonlinear structures are discussed. Properties of Faá di Bruno polynomials are extensively explored in this construction. Applications of our method are given for the Conformal Affine Toda model, WZNW models and discrete KP approach to Toda lattice chain.

28 pages, IFT-P/020/92-SAO-PAULO, Latex

References in corpus (3)

• Nonlinear ${\hat{W}}_{\infty }$ Current Algebra in the SL(2,R)/U(1) Coset Model
• Comments on Two-Loop Kac-Moody Algebras
• A New Deformation of W-Infinity and Applications to the Two-loop WZNW and Conformal Affine Toda Models

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• Matrix models without scaling limit
• Virasoro Symmetry of Constrained KP Hierarchies
• Solitons, Tau-functions and Hamiltonian Reduction for Non-Abelian Conformal Affine Toda Theories
• R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence
• Multi-field representations of KP hierarchies and multi-matrix models
• On the constrained KP hierarchy
• Supersymmetric Two-Boson Equation: Bilinearization and Solutions
• Connection between the Affine and Conformal Affine Toda Models and their Hirota's Solution
• Constrained KP Models as Integrable Matrix Hierarchies
• Construction of KP Hierarchies in Terms of Finite Number of Fields and their Abelianization
• Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies
• Integrable Hierarchy for Multidimensional Toda Equations and Topological-Anti-topological Fusion
• Properties of Nonlocal Charges in the Supersymmetric Two Boson Hierarchy
• Affine Lie Algebraic Origin of Constrained KP Hierarchies
• The Constrained KP Hierarchy and the Generalised Miura Transformation
• The sTB-B Hierarchy
• On Discrete Symmetries of the Multi-Boson KP Hierarchies
• Generalized NLS Hierarchies from Rational $W$ Algebras
• Classical Extended Conformal Algebras Associated with Constrained KP Hierarchy
• Hamiltonian Structures of the Multi-Boson KP Hierarchies, Abelianization and Lattice Formulation
• Toda lattice realization of integrable hierarchies
• On Coset Reductions of KP Hierarchies
• On Non-Linear W-Infinity Symmetry of Generalized Liouville and Conformal Toda Models