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Results in Mathematics

, 74:11 | Cite as

Finite Genus Solutions to the Coupled Burgers Hierarchy

  • Xianguo Geng
  • Wei Liu
  • Bo XueEmail author
Article
  • 57 Downloads

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.

Keywords

Finite genus solutions coupled Burgers hierarchy trigonal curves 

Mathematics Subject Classification

35Q51 35Q55 37K10 37K20 

Notes

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouPeople’s Republic of China
  2. 2.Department of Mathematics and PhysicsShijiazhuang Tiedao UniversityShijiazhuangPeople’s Republic of China

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