Semi-direct sums of Lie algebras and discrete integrable couplings

Details Semi-direct sums of Lie algebras and discrete integrable couplings Semi-direct sums of Lie algebras and discrete integrable couplings

2006-03-27

arxiv.org/abs/nlin/0603064v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages

Scientific paper

10.1016/j.physleta.2005.09.087

A relation between semi-direct sums of Lie algebras and integrable couplings of lattice equations is established, and a practicable way to construct integrable couplings is further proposed. An application of the resulting general theory to the generalized Toda spectral problem yields two classes of integrable couplings for the generalized Toda hierarchy of lattice equations. The construction of integrable couplings using semi-direct sums of Lie algebras provides a good source of information on complete classification of integrable lattice equations.

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