Abstract
It is shown that the algebra valued by the generalized Lax representation of nonlinear (evolution) system, i.e. the prolongation algebra y×D(λ), is in fact Kac-Moody type algebra where y is a finite dimensional Lie algebra and D(λ) the domain of value of the spectral parameter λ. The realization of the Kac-Moody algebra in a kind of 2 dimensional nonlinear (evolution) systems has been given by means of the realization of the Kac-Moody algebra in the principal chiral model due to Dolan.
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