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

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (06): 1333-1338.

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

牛艳秋¹, 杨双羚^1,2, 许明星²

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

收稿日期:2019-05-14 出版日期:2019-11-26 发布日期:2019-11-21
通讯作者: 杨双羚 E-mail:550913482@qq.com

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

NIU Yanqiu^1, YANG Shuangling^1,2, XU Mingxing²

1. Department of Foundation, Jilin University of Architecture and Technology, Changchun 130114, China;
2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2019-05-14 Online:2019-11-26 Published:2019-11-21
Contact: YANG Shuangling E-mail:550913482@qq.com

摘要/Abstract

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R³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.

关键词: 不变代数曲面, 双Hamilton结构, Poincaré紧致化

Abstract: 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 Poincaré compactification technique in R³ to describe the dynamic behavior at infinity of the system.

Key words: invariant algebraic surface, biHamiltonian structure, Poincaré compactification

中图分类号:

O175.12

牛艳秋, 杨双羚, 许明星. 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[J]. 吉林大学学报(理学版), 2019, 57(06): 1333-1338.

NIU Yanqiu, YANG Shuangling, XU Mingxing. Invariant Algebraic Surfaces, Hamiltonian Structures andDynamic Behavior at Infinity for ThreeWave Interaction Model[J]. Journal of Jilin University Science Edition, 2019, 57(06): 1333-1338.