We study the nonlinear dynamics of a three-dimensional Bose-Einstein condensate (BEC) excited by a vortex ring phase imprinting. We identify independent, integrated, and stationary modes of the center-of-mass oscillation of the condensate with respect to the vortex ring movement. We show that the oscillation amplitude of the center-of-mass of the condensate depends strongly on the initial radius of the vortex ring, the nonlinear inter-atomic interaction, and the aspect ratio of the trap, while the oscillation frequency is fixed and equals to the frequency of the harmonic trap in the direction of the ring movement. However, when applying Kelvin wave perturbations on the vortex ring, the center-of-mass oscillation of the BEC is changed non-trivially with respect to the perturbation modes, the long-scale perturbation strength as well as the wave number of the perturbations. The parity of the wave number of the Kelvin perturbations plays an important role on the mode of the center-of-mass oscillation of the condensate.

我们研究了由涡环相印激发的三维玻色-爱因斯坦凝聚物（BEC）的非线性动力学。我们确定了冷凝水质心相对于涡环运动的独立，积分和静止模式。我们表明，凝结质心的振荡幅度在很大程度上取决于涡流环的初始半径，非线性原子间相互作用以及阱的长宽比，而振荡频率是固定的并且等于沿振铃运动方向的谐波陷波频率。但是，当在开环上应用开尔文波扰动时，BEC的质心振荡相对于扰动模式会发生不平凡的变化，长期的扰动强度以及扰动的波数。开尔文摄动的波数奇偶性对冷凝液质心振荡的模式起着重要作用。