Abstract:
A Lenard equation is introduced, its two special solutions are given. One is used to
derive an exceptional Dirac hierarchy, the other is applied to construct the generation
function. The generation function yields conserved integrals of the Dirac Hamiltonian
system, and defines an algebraic curve. Based on the theory of algebraic curve,
the Dirac Hamiltonian system is proved to be integrable, the algebraic-geometric
solutions of the Dirac hierarchy are obtained.
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