一种非线性方程的强非线性共振的转迁集

The Transition Sets for a Class of Nonlinear Equation with Strongly Nonlinear Resonance

运用多尺度法和改进的L-P方法,通过引入参数变换把较大的摄动参数ε转换成小参数α,从而使讨论的非线性方程可用多尺度法和L-P方法求其近似解。求出了该方程亚谐共振（即k=1/2）时的分岔响应方程和转迁集。

In the paper the improved L- P method and multiple scale method were used, and parameter transformation weve introduced to switch larger parameter to smaller parameter so that the improved L- P method and multiple scale method can be used to work out the approximate solution of the nonlinear equation discussed. Furthermore, the branching response equation and transition sets of the equations were obtained for 1/2 subharmonic resonance.