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arXiv · 0711.1147

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

Wen-Xiu Ma
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Abstract

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant $γ$ 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.

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Wen-Xiu Ma. 2007-11-07. A discrete variational identity on semi-direct sums of Lie algebras. https://doi.org/10.1088/1751-8113/40/50/010

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