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TMF, 2017, Volume 190, Number 1, Pages 21–47 (Mi tmf9105)  

This article is cited in 1 scientific paper (total in 1 paper)

Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy

Xianguo Geng, Xin Zeng

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, People's Republic of China

Abstract: We develop a method for constructing algebro-geometric solutions of the Blaszak–Marciniak {(}BM{\rm)} lattice hierarchy based on the theory of trigonal curves. We first derive the BM lattice hierarchy associated with a discrete $(3{\times}3)$-matrix spectral problem using Lenard recurrence relations. Using the characteristic polynomial of the Lax matrix for the BM lattice hierarchy, we introduce a trigonal curve with two infinite points, which we use to establish the associated Dubrovin-type equations. We then study the asymptotic properties of the algebraic function carrying the data of the divisor and the Baker–Akhiezer function near the two infinite points on the trigonal curve. We finally obtain algebro-geometric solutions of the entire BM lattice hierarchy in terms of the Riemann theta function.

Keywords: Blaszak–Marciniak lattice, algebro-geometric solution, trigonal curve

Funding Agency Grant Number
National Natural Science Foundation of China 11331008
This research was supported by the National Natural Science Foundation of China (Grant No. 11331008).


DOI: https://doi.org/10.4213/tmf9105

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English version:
Theoretical and Mathematical Physics, 2017, 190:1, 18–42

Bibliographic databases:

Document Type: Article
Received: 14.11.2015
Revised: 03.03.2016

Citation: Xianguo Geng, Xin Zeng, “Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy”, TMF, 190:1 (2017), 21–47; Theoret. and Math. Phys., 190:1 (2017), 18–42

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Geng X., Liu W., Xue B., “Finite Genus Solutions to the Coupled Burgers Hierarchy”, Results Math., 74:1 (2019), UNSP 11  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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