高维可积模型构造和解析解  

High-dimensional integrable model construction and analytical solution

作　　者：林机[1] LIN Ji(Department of Physics,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学物理系,浙江金华321004

出　　处：《宁波大学学报（理工版）》2020年第5期3-7,共5页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(10571086).

摘　　要：根据Virasoro可积性(具有无限维无中心Virasoro型对称代数意义下的可积性)的定义建立了一种系统构造(3+1)维Virasoro可积模型的方法.利用广义Virasoro型对称代数的每一种具体实现,可以得到大量的高维Virasoro意义下可积模型.同时,还获得了具有共形不变性、Painlevé和Lax对意义下的高维可积方程.最后,研究了部分方程的解析解.On the basis of the definition of Virasoro’s integrability(with infinite dimensional and no-center Virasoro-type symmetric algebra),the method of constructing higher-dimension Virasoro of integrable model is presented.A large number of higher-dimensions integrable models can be obtained through each of specific realizations of the generalized Virasoro-type symmetric algebra.In addition,the high-dimensional integrable equations with conformally invariance,Painlevéand Lax pair are also obtained.Finally,the analytical solutions of some equations are studied.

关 键 词：Virasoro对称代数 高维模型 解析解 可积性 

分 类 号：O411[理学—理论物理]