负能模式在非线性不稳定性中的作用再探

讨论了本征矢量的非线性变化说明相对于定态波每一个非线性本征频率允许向前和向后传播，与线性情形比较，它们的本征矢量在傅里叶空间发生了偏转根据向前和向后的扰动本征矢量的相对强度可以定义非线性条件下的正能和负能模式按照这一定义，本文再探了负能模式在非线性不稳定性中的作用，结果证实了文献1，2]的推断波包的双稳滞后分岔与一个共振负能模式向正能模式转变相联系，这个转变伴随着本征扰动矢量在参数空间的不连续性；波包的Hopf分岔与一对具有正能和负能模式的本征扰动矢量的重联和它们的能态转变有关随着非线性增强，共振的正能和负能模式先后改变能态，因此存在两个模式同时为负能的参数区，它与Hopf失稳参数区符合这一结果强烈地支持负能模式的激发引起非线性(Hopf)不稳定性的猜想 关键词：

FURTHER EXPLORATION ON THE EFFECT OFNEGATIVE-ENERGY MODES IN THENONLINEAR INSTABILITIES

The nonlinear variations of the eigenvectors are discussed on the basis of Ref. 1, 2]. Itis shown that relative to a steady wave the nonlinear eigen frequency allows for both forwardand backward transports. Their eigenvectors deflect in the Fourier space as compared'to thelinear case. The positive (P-) and negative (N-) energy modes can be defined in the nonlin ear case according to the relative strength of the forward and backward eigenvectors of theperturbations. Based on this definition the effect of N-mode on the nonlinear instabilities isfurther studied. The results are in consistency with the conclusion in Ref. 1, 2 ]. The bista-bility of wavepacket is associated with the transition of a resonance N-mode to a p-mode, inparticular its eigenvector is discontinuous in the parameter space; The Hop f bifurcation of asteady wavepacket is associated with the resonance of a N-mode to a p-mode. As a result re-connections occur between their eigenvectors of forward and backward perturbations respec-tively. With the increase of nonlinearity, the p-mode first and the N-mode following nextchange their energy types. Consequently there exists a parameter regime where both modesbecome N-type. This regime coincides with that of the Hop f bifurcation. This fact stronglysupports the conjecture that the excitation of N-modes induces the nonlinear (Hopf) bifurcation.