五次非线性Schr?dinger方程的非横截异宿链  

Non-transversal heteroclinic chain in the quintic nonlinear Schr?dinger equation

作　　者：陈爱永[1,2] 邓同杰 闫东风 Aiyong Chen;Tongjie Deng;Dongfeng Yan

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林541004 [2]湖南第一师范学院数学与计算科学学院,长沙410205 [3]郑州大学数学与统计学院,郑州450001

出　　处：《中国科学：数学》2018年第12期1791-1802,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11671107,11601487);广西自然科学基金(批准号:2015GXNSFGA139004)资助项目.

摘　　要：非横截扩散看起来类似Arnold扩散,但它不同于Arnold扩散,非横截扩散可能出现在可积系统中,而Arnold扩散只能出现在非可积系统中.本文研究五次非线性Schr?dinger方程的非横截异宿链的存在性,基于一个约化的有限维常微分系统—Toy模型系统,构造了该系统的非横截异宿链,给出了非横截异宿轨道的显式表达式.Non-transversal diffusion seems similar to the Arnold diffusion,but it is a different phenomenon since it could be applied to integrable systems in contrast to the Arnold diffusion,which is a phenomenon that only takes place in non integrable systems.In this paper,the existence of the non-transversal heteroclinic chain in the quintic nonlinear SchrSdinger equation is studied.Based on a finite dimensional system of ordinary differential equations,the Toy model system associated with the quintic nonlinear SchrSdinger equation,we construct the non-transversal heteroclinic chain of the Toy model system.The explicit expression for the dynamics of the heteroclinic is given.

关 键 词：SCHRODINGER方程 KAM(Kolmogorov-Arnold-Moser)理论 Arnold扩散 异宿轨道 

分 类 号：O175[理学—数学]