The research of longtime dynamic behavior in weakly damped forced KdV equation

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.