L. Bonora et al., THE INTEGRABLE HIERARCHY CONSTRUCTED FROM A PAIR OF KDV-TYPE HIERARCHIES AND ITS ASSOCIATED W-ALGEBRA, Communications in Mathematical Physics, 175(1), 1996, pp. 177-202
For any two arbitrary positive integers ''n'' and ''m'', using the m(t
h) 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 second
Hamiltonian structure of the (n,m)(th) KdV hierarchy (called W(n, m) a
lgebra) is isomorphic via a Miura map to the direct sum of a W-m-algeb
ra, a W-n+m-algebra and an additional U(1) current algebra. In turn, f
rom the latter, we can always construct a representation of a W-infini
ty-algebra.