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

Paolo Casati·Alberto Della Vedova·Giovanni Ortenzi
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Abstract

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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Paolo Casati, Alberto Della Vedova, Giovanni Ortenzi. 2006-10-16. The Soliton Equations associated with the Affine Kac-Moody Lie Algebra G_2^{(1)}. https://doi.org/10.1016/j.geomphys.2007.11.012

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