Kac-moody lie algebras and soliton equations: II. Lax equations associated with A1(1)

The soliton equations associated with sl(2) eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment; they are shown to be generated by a single family of commuting Hamiltonians on a subalgebra of the loop algebra of sl(2). The conserved densities and fluxes of the usual ANKS hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems. The Hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment.