多尺度方法在强非线性系统中应用的一个注释

Note of the Applications of Multiple Scales in Strongly Non-linear System

多尺度法在求解非线性系统时,目前所得到的结果多集中在弱非线性系统上。论文对多尺度法进行了改进。对强非线性杜芬系统进行了变换,得到了强非线性杜芬系统存在3个解的结论,其中大的和小的是稳定的,中间的是不稳定的,物理上实现哪个稳定运动取决于初始条件。

The solutions obtained based on muhiople scale scheme when dealing with nonlinear system are mainly in the weak nonlinear system. Some innovations are made to the multiple scale scheme. Three solutions have been obtained by implementing transform to nonlinear Dufen System in which the largest and the smallest are steady while the intermediate one is unsteady. The nontrivial steady motion depends on the initial condition