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

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

2007-11-07

arxiv.org/abs/0711.1147v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages

Scientific paper

10.1088/1751-8113/40/50/010

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.

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