Kac-Moody symmetry of generalized nonlinear Schrödinger equations (Q1100639)

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