一族拉克斯可积晶格方程  

A Hierarchy of Lax Integrable Lattice Equations

作　　者：吴迪[1] 郭敏[1] WU Di GUO Min(Shandong University of Science and Technology, Qingdao 2 6 6 5 9 0, Chin)

机构地区：[1]山东科技大学,山东青岛266590

出　　处：《潍坊学院学报》2016年第6期32-35,共4页Journal of Weifang University

摘　　要：孤立子理论的研究不断发展,在很多科学领域中都存在孤立子以及与孤立子理论密切联系的问题,可积耦合系统是在研究无中心的Virasoro对称代数或孤立子方程时产生的。人们已经找到多种求可积耦合的方法:1.摄动方法;2.扩大对应的Lax对的方法;3.扩展新的loop代数的方法;4.利用半直和李代数的方法,等等。提出一个离散的矩阵谱问题,由离散零曲率方程推导出一类新的可积晶格方程族。那么,获得的晶格方程族的拉克斯可积性得到证明。Soliton theory research is developing in many scientific： fields and there exists soliton and soliton theory closely re-lated problems, integrable coupling system is in the center of the study without Virasoro algebra or symmetrically soliton e- quation. People have found many integrable coupling methods： one. the perturbation method; two, expand the corresponding method of Lax on three,extend new loop algebra of the methods four,the use of a half straight and Lie algebra method and so on. A discrete matrix spectral problem are presented, a novel family of integrable lattice equations is derived from the dis-- crete zero curvature equations. Then, Lax integrability for the obtained family is demonstrated.

关 键 词：离散谱问题 离散零曲率方程 可积晶格方程 

分 类 号：O175[理学—数学]