一类非线性奇摄动方程的渐近解

Asymptotic solution for a class of nonlinear singularly perturbed equation

讨论了一类二阶弱非线性常微分方程,利用Lindstedt-Poincare法,引入参量变换,消去形式解中出现的长期项,得到了解的一阶一致有效的渐近展开式.再用多重尺度法,引入多个变量尺度,把原常微分方程转化为几个相应的偏微分方程,再根据不出现长期项的原则,构造了解的渐近展开式.最后,比较了上述两种方法得到的解的展开式,得到了相同的结果.

A class of weakly nonlinear ordinary equation for second order is considered. By using the Lindatedt-Poincare method, introducing the transformation of parameter and eliminating the secular terms in the formal solution, the first order uniformly valid asymptotic expansion is obtained. And by using the multi-scales method, introducing many scale variables and in light of the principle for without appearing the secular terms, the asymptotic expansion of the solution is constructed too. Comparison between the two expansions leads to the same results.