期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
卷 39, 期 34, 页码 10787-10801出版社
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/39/34/013
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The trace variational identity is generalized to zero curvature equations associated with non-semi-simple Lie algebras or, equivalently, Lie algebras possessing degenerate Killing forms. An application of the resulting generalized variational identity to a class of semi-direct sums of Lie algebras in the AKNS case furnishes Hamiltonian and quasi-Hamiltonian structures of the associated integrable couplings. Three examples of integrable couplings for the AKNS hierarchy are presented: one Hamiltonian and two quasi-Hamiltonian.
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