弱阻尼KdV方程中长期动力学行为研究*
The Research of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation
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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.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.
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