一个新非线性可积晶格族和它们的可积辛映射  

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

作　　者：张宁 夏铁成[1] 

机构地区：[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

出　　处：《数学物理学报（A辑）》2017年第5期814-824,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271008;61072147);山东省高校科研项目(J14LI58)~~

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.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.

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 

分 类 号：O175[理学—数学]