Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
WX Ma, M Chen - Journal of Physics A: Mathematical and …, 2006 - iopscience.iop.org
WX Ma, M Chen
Journal of Physics A: Mathematical and General, 2006•iopscience.iop.orgThe 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.
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.
Abstract
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.
iopscience.iop.org