Kac-moody lie algebras and soliton equations. III. Stationary equations associated with A₁⁽¹⁾

The Hamiltonian structure of stationary soliton equations associated with the AKNS eigenvalue problem is derived in two ways. First, it is shown to arise from the Kostant-Kirillov symplectic structure on a coadjoint orbit in an infinite-dimensional Lie algebra. Second, it is obtained as the restriction to a finite-dimensional manifold of the infinite-dimensional Hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter.