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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 algebras and the relation between two fundamental nonlinear structures are discussed. Properties of Fa√° 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:
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q58Other completely integrable PDE (MSC2000)
81R10Infinite-dimensional groups and algebras motivated by physics
81T40Two-dimensional field theories, conformal field theories, etc.