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. © 2007 Elsevier Ltd. All rights reserved.
The soliton equations associated with the affine Kac-Moody Lie algebra $G\sp {(1)}\sb 2$
ORTENZI, GIOVANNI
2008-01-01
Abstract
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. © 2007 Elsevier Ltd. All rights reserved.
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