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Algebro-geometric solutions of the modified Jaulent–Miodek hierarchy

Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

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Deng-Shan Wang

https://orcid.org/0000-0002-4184-3130

Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

E-mail Address: dswang@bnu.edu.cn

Corresponding author.

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, and

Peng Zhao

College of Science, Shanghai Maritime University, Shanghai 201306, P. R. China

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https://doi.org/10.1142/S0219887823502390Cited by:2 (Source: Crossref)

Abstract

According to the polynomial recursion formalism, the modified Jaulent–Miodek hierarchy is derived in a standard way. The first two nontrivial members in the modified Jaulent–Miodek hierarchy are listed correspondingly. Based on the squared eigenfunctions, an algebraic curve $κ_{n}$ and a Riemann surface $S$ with arithmetic genus $n$ are introduced, then the Dubrovin-type equations are obtained naturally. With the help of the conservation laws, the Baker–Akhiezer functions are defined. Finally, the asymptotic properties of the Baker–Akhiezer functions are analyzed, from which the algebro-geometric solutions of the modified Jaulent–Miodek hierarchy are constructed in term of the Riemann theta function.

Keywords:

AMSC: 35C05, 37K40, 35Q51

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