摘要
利用无穷维动力系统理论、不变流形、纤维丛以及Melnikov分析的方法,证明了周期边界条件下Ginzburg landau方程存在整体吸引子,并估计该吸引子的维数.在偶周期边界条件下,在可积非线性Schro··dinger方程摄动系统中证明了一对非平凡对称的同宿轨道的存在性.结果表明整体吸引子是由同宿轨道的保持引起的.
The existence of a global attractor for Ginzberg-Landau equations in the space periodic case is proved; the dimensions of the attractor are estimated. The persistence of homoclinic orbits for certain perturbation of the integrable nonlinear (Schro(··) dinger) equation under even periodic boundary conditions is established. The method is based on invariant manifolds,foliations and Melnikov analysis.The results show that the complex structure of the global attractor, i.e. , space-time chaos results from the persistence of homoclinic orbits.
出处
《江苏大学学报（自然科学版）》
EI
CAS
2004年第3期224-227,共4页
Journal of Jiangsu University：Natural Science Edition
基金
国家自然科学基金资助项目(10372054)
关键词
整体吸引子
同宿轨道
孤立子
global attractor
homoclinic orbits
soliton
