微扰法解由正弦波驱动的非线性漂移波的分岔

A PERTURBATION METHOD FOR THE NONLINEAR DRIFT WAVES DRIVEN BY A SINUSOIDAL WAVE

在以驱动波相速度运动的坐标系中,用微扰法讨论。在正弦波驱动下的非线性漂移波的分波方程。结果表明,在文献[1]中观察到的波包能量的滞后分岔和由定态向周期态的分岔可以统一地解析描述,它们分别对应某一非线性共振模式在时间维上的鞍结点分岔和Hopf分岔。波包能量失稳的频率是该模式的本征频率,除多普勒移动外,它的大小还因非线性效应而不同于其在实验室坐标系中的线性值。

The nonlinear drift-wave equation driven by a sinusoidal wave is discussed in a coordinate system moving in the driving phase speed. It is shown that the hysteretic jump of the wave energy and its transition to periodic motions from the steady state can be described integrately by the perturbation method proposed in this paper. The saddle-node and Hopf bifurcations of certain resonance mode are responsible for them respectively. The frequency of the periodic oscillatory wave energy is relevant to the eigen-frequency of the system, which is different from the one in the laboratory frame due to the Doppler shift and the nonlinea-rity.