科研之友
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摘要
Resorting to the Lenard recursion equations, we derive the Newell hierarchy associated with a 3 x 3 matrix spectral problem and establish Dubrovin-type equations in terms of the introduced trigonal curve Km-1 of arithmetic genus m - 1. Based on the theory of trigonal curve, we construct the corresponding Baker-Akhiezer functions and meromorphic functions on Km-1. The known zeros and poles for the Baker-Akhiezer functions and meromorphic functions allow one to find their theta function representations, from which we give algebro-geometric constructions of quasi-periodic flows of the Newell hierarchy and their explicit theta function representations.
