一类三波作用模型的不变代数曲面、Hamilton结构及无穷远动力学行为  

Invariant Algebraic Surfaces,Hamiltonian Structures and Dynamic Behavior at Infinity for Three-Wave Interaction Model

作　　者：牛艳秋 杨双羚 许明星 NIU Yanqiu;YANG Shuangling;XU Mingxing(Department of Foundation,Jilin University of Architecture and Technology,Changchun 130114,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林建筑科技学院基础部,长春130114 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2019年第6期1333-1338,共6页Journal of Jilin University:Science Edition

基　　金：吉林省科技发展计划项目(批准号:20170520055JH)

摘　　要：首先利用代数几何中的消除理论给出一类三波作用模型存在不变代数曲面的充分条件;其次,构造出该系统无穷多个Hamilton-Poisson结构,即该系统是双Hamilton的;最后,利用R^3中的Poincaré紧致化技巧完整刻画该系统在无穷远处的动力学行为.Firstly,by using the elimination theory in algebraic geometry,we gave sufficient conditions for the existence of invariant algebraic surfaces in a three-wave interaction model.Secondly,we constructed an infinite number of Hamiltonian-Poisson structures of the system,the system was bi-Hamiltonian.Finally,we used the Poincarécompactification technique in R3 to describe the dynamic behavior at infinity of the system.

关 键 词：不变代数曲面 双HAMILTON结构 Poincaré紧致化 

分 类 号：O175.12[理学—数学]