Kac-Moody symmetry of generalized non-linear Schrödinger equations

The classical non-linear Schrödinger equation associated with a symmetric Lie algebra g{script}=k⊕m is known to possess a class of conserved quantities which from a realization of the algebra k⊗ℂ [λ]. The construction is now extended to provide a realization of the Kac-Moody algebra k⊗ℂ[λ, λ^-1] (with central extension). One can then define auxiliary quantities to obtain the full algebra g{script}⊗ℂ[λ, λ^-1]. This leads to the formal linearization of the system.