Abstract
It is shown how to construct infinitely many conserved quantities for the classical non-linear Schrodinger equation associated with an arbitrary Hermitian symmetric spaceG/K. These quantities are non-local in general, but include a series of local quantities as a special case. Their Poisson bracket algebra is studied, and is found to be a realization of the “half” Kac-Moody algebrakR ⊗ ℂ [λ], consisting of polynomials in positive powers of a complex parameter λ which have coefficients in the compact real form ofk (the Lie algebra ofK).
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