Symmetries of the Ablowitz–Kaup–Newell–Segur hierarchy

Abstract

Nonlocal symmetries of the Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy are introduced and it is shown that the symmetry algebra of the AKNS hierarchy is isomorphic to the loop algebra sl(2,C)⊗C[λ, λ−1]. As a special case, the symmetry algebra of the nonlinear Schrödinger equation is determined and is shown to be isomorphic to the loop algebra su(2)⊗R[λ, λ−1] or g⊗R[λ, λ−1] corresponding to the sign of the nonlinear term, where g is a noncompact real form of sl(2,C).