Abstract
The coupled Burgers hierarchy is derived with the aid of Lenard recursion sequences. Based on the characteristic polynomial of Lax matrix, a trigonal curve of arithmetic genus $$m-2$$ is introduced, from which the meromorphic functions $$\phi _2,\phi _3$$ and the Baker–Akhiezer $$\psi $$ function are defined. The finite genus solutions for the coupled Burgers hierarchy are achieved by using asymptotic expansion of $$\phi _2,\phi _3$$ and their Riemann theta function representation.
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