The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated $W$ algebra

Abstract

For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV hierarchy). The $W$--algebra associated to the \shs\, of the $(n,m)$--th KdV hierarchy (called $W(n,m)$ algebra) is isomorphic via a Miura map to the direct sum of $W_m$--algebra, $W_{n+m}$--algebra and an additional $U(1)$ current algebra. In turn, from the latter, we can always construct a representation of $W_{\infty }$--algebra.

26p, latex, BONN--TH-94-17, SISSA-ISAS-118/94/EP, AS-ITP-94-43, revised version with additions

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• Toward the construction of N=2 supersymmetric integrable hierarchies
• Integrable Coupled KdV Systems
• Extended N=2 supersymmetric matrix (1,s)-KdV hierarchies
• On integrability of some bi-Hamiltonian two field systems of PDE
• Hydrodynamic Reductions of Dispersionless Harry Dym Hierarchy
• Super KP equations and Darboux transformations: another perspective on the Jacobian Super KP hierarchy
• The constrained modified KP hierarchy and the generalized Miura transformations
• Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy