mKdV-Burgers方程长期动力学行为的数值分析

Numerical Analysis of Longtime Dynamic Behavior of mKdV-Burgers Equation

研究一类称之为mKdV Burgers方程的非线性演化方程 为了得到这一方程的长期动力学行为,利用惯性流形和近似惯性流形理论,在已经证明这一类方程的近似惯性流形存在的基础上,给出低模态下周期边界条件的mKdV Burgers方程近似惯性流形的约化形式,并在三模态下作数值分析。

Approximate inertial manifold(AIM) is a finite dimensional smooth manifold which makes all the orbits enter the neighbor of the manifold after certain time, especially, attractors are included in the AIM. A special type of nonlinear evolutionary equation, mKdVBurgers equation, is studied.To find the longtime dynamic behavior of mKdVBurgers equation, by the theory of IM and AIM, and based on the existed approximate inertial manifolds in this type of nonlinear evolutionary equations, the reduced form of approximate inertial manifold of mKdVBurgers equation associated with periodic boundary conditions under low models is derived. The result of numerical analysis under three modes is also given.