The Soliton Equations associated with the Affine Kac-Moody Lie Algebra G_2^{(1)}

Details The Soliton Equations associated with the Affine Kac-Moody Lie Algebra G_2^{(1)} The Soliton Equations associated with the Affine Kac-Moody Lie Algebra G_2^{(1)}

2006-10-16

arxiv.org/abs/nlin/0610034v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, no figures. v2: some typos corrected

Scientific paper

We construct in an explict way the soliton equation corresponding to the affine Kac--Moody Lie algebra $G_2^{(1)}$ 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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