一个新非线性可积晶格族和它们的可积辛映射

数学物理学报 ›› 2017, Vol. 37 ›› Issue (5): 814-824.

一个新非线性可积晶格族和它们的可积辛映射

张宁^1,2, 夏铁成¹

1. 上海大学数学系上海 200444;
2. 山东科技大学(泰安校区)基础课部山东泰安 271019

收稿日期:2016-12-07 修回日期:2017-04-21 出版日期:2017-10-26 发布日期:2017-10-26
通讯作者: 夏铁成,E-mail:xiatc@shu.edu.cn E-mail:xiatc@shu.edu.cn
作者简介:张宁,E-mail:zhangningsdust@126.com
基金资助:
国家自然科学基金（11271008，61072147）和山东省高校科研项目（J14LI58）

A New Integrable Nonlinear Lattice Equation Hierarchy and Their Integrable Symplectic Map

Zhang Ning^1,2, Xia Tiecheng¹

1. Department of Mathematics, Shanghai University, Shanghai 200444;
2. Department of Basical Courses, Shandong University of Science and Technology, Shandong Taian 271019

Received:2016-12-07 Revised:2017-04-21 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the NSFC (11271008, 61072147) and the Project of Shandong Province Higher Educational Science and Technology Program (J14LI58)

摘要/Abstract

摘要： 该文引入一个离散特征值问题，导出一族离散可积系，建立了它们的Hamilton结构，证明了它们Louville可积性.通过谱问题双非线性化，得到了一个可积辛映射与一族有限维完全可积系，最后给出了离散可积系统解的表示.

关键词: 离散可积系, Hamilton结构, Louville可积性, 双非线性化, 可积辛映射

Abstract: In this paper, a discrete matrix spectral problem is introduced and a hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established, and it is shown that the resulting discrete systems are all Liouville integrable. Through binary nonlinearization method, the Bargmann symmetry constraint and a family of finite-dimension completely integrable systems are obtained. Finally, the representation of solutions for the discrete integrable systems are given.

Key words: Discrete integrable system, Hamiltonian structure, Liouville integrability, Bargmann symmetry constraint

中图分类号:

O175

张宁, 夏铁成. 一个新非线性可积晶格族和它们的可积辛映射[J]. 数学物理学报, 2017, 37(5): 814-824.

Zhang Ning, Xia Tiecheng. A New Integrable Nonlinear Lattice Equation Hierarchy and Their Integrable Symplectic Map[J]. Acta mathematica scientia,Series A, 2017, 37(5): 814-824.

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