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On two-current realization of KP hierarchy. (English) Zbl 0941.37525
Summary: 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 ${W}_{\infty }$ algebras and the 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.
##### MSC:
 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 35Q58 Other completely integrable PDE (MSC2000) 81R10 Infinite-dimensional groups and algebras motivated by physics 81T40 Two-dimensional field theories, conformal field theories, etc.