Abstract
AbstractA non-semisimple matrix loop algebra is presented, and a class of zero curvature equations over this loop algebra is used to generate bi-integrable couplings. An illustrative example is made for the Dirac soliton hierarchy. Associated variational identities yield bi-Hamiltonian structures of the resulting bi-integrable couplings, such that the hierarchy of bi-integrable couplings possesses infinitely many commuting symmetries and conserved functionals.
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