弱阻尼KdV方程中长期动力学行为研究<sup>*</sup>

弱阻尼KdV方程中长期动力学行为研究^*

基金项目: *国家自然科学基金;机械工业部科技基金

1.
Department of Mathematics and Physics Jiangsu University of Science and Technology, Zhenjiang 212013, P. R. China;
2.
Wuxi Light Industry Institute, Wuxi 214000, P. R. China

摘要: 证明了周期边界条件下弱阻尼KdV方程存在近似惯性流形．该流形使吸引子被确切定义的有限维光滑流形逼近．并由此概念引出新的数值方法很好地用于研究动力系统长期行为．
- 近似惯性流形 /
- 弱阻尼KdV方程 /
- 动力系统 /
- 吸引子
Abstract: It is presented that there exists approximate inertial manifolds in weakly damped forced Kdv equation with with periodic boundary conditionsIIbns.The approximate inertial manifolds provide approximant of the attractror by finite dimensional smooth manifolds which are exphcitly defined And the concepl leads to new numerical schemes which are well adapted to the longtime behavior of dynamical system.
- approximate inertial manifold /
- weakly damped forced KdV equation /
- dynamical system /
- attractor

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