离散可积系统:多维相容性  

Discrete integrable systems: Multidimensional consistency

作　　者：张大军[1] Zhang Da-Jun(Department of Mathematics,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学数学系

出　　处：《物理学报》2020年第1期19-30,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11875040,11631007)资助的课题~~

摘　　要：对比已有完善而系统理论的微分方程领域,差分方程理论尚处于发展之中.近年来离散可积理论的进展,带来了差分方程理论的革命.多维相容性是伴随离散可积系统研究出现的新的概念,作为对离散可积性的一种理解,提供了构造离散可积系统的B?cklund变换、Lax对和精确解的工具.本文旨在综述多维相容性的概念及其在离散可积系统研究中的应用.In contrast to the well-established theory of differential equations,the theory of difference equations has not quite developed so far.The most recent advances in the theory of discrete integrable systems have brought a true revolution to the study of difference equations.Multidimensional consistency is a new concept appearing in the research of discrete integrable systems.This property,as an explanation to a type of discrete integrability,plays an important role in constructing the B?cklund transformations,Lax pairs and exact solutions for discrete integrable system.In the present paper,the multidimensional consistency and its applications in the research of discrete integrable systems are reviewed.

关 键 词：离散可积系统 多维相容性 

分 类 号：O17[理学—数学]