A discrete variational identity on semi-direct sums of Lie algebras

Abstract

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant $\gamma$ involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy.

arXiv comment18 pages

References in corpus (7)

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• Semi-direct sums of Lie algebras and discrete integrable couplings
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• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
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