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

We construct in an explicit way the soliton equations corresponding to the affine Kac–Moody Lie algebra G2(1) together with their bi-Hamiltonian structure. Moreover the Riccati equation satisfied by the generating function of the commuting Hamiltonian densities is also deduced. Finally we describe a way to deduce the bi-Hamiltonian equations directly in terms of this latter function.