The soliton equations associated with the affine Kac–Moody Lie algebra G2(1)

Abstract

We construct in an explict way the soliton equation corresponding to the affine Kac-Moody Lie algebra G (1) 2 together with their bihamiltonian structure. Moreover the Riccati equation satisfied by the generating function of the commuting Hamiltonians densities is also deduced. Finally we describe a way to deduce the bihamiltonian equations directly in terms of this latter functions

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