长短波方程组的近似惯性流形

Approximate Inertial Manifolds for Long-short Equations

研究了动力学中具有耗散性的非线性长短波方程组的长时间行态 ,运用算子投射和算子特征值等方法 ,构建了其线性的和非线性的多种近似惯性流形 。

In this paper, the long time behavor of the dissipative nonlinear long-short equations was studied in dynamics. By applying projecting operator and the operator eigenvalue methods, several linear and nonlinear approximate inertial manifolds of the system were constructed. And it is proved that arbitary trajectory of the long-short equations goes into a small neighbourhood of the approximate inertia manifolds after long time.