Spatiotemporal bifurcations of a parametrically excited solitary wave.
The bifurcation behaviors of a parametrically excited solitary wave are investigated via Faraday's water tank experiment. It is observed that, as the driving frequency fd is decreased or/and the driving amplitude Ad is increased, the standing (but vertically oscillatory) solitary wave becomes modulationally unstable, leading to the temporal modulation of the vertical oscillation and the emergence of very low subharomic components on the frequency spectrum. Further lowering fd or/and increasing Ad will cause the modulational oscillation unstable and then, the peak of the solitary wave becomes rocking along the trough in the longitudinal direction. These bifurcations also give rise to the emission of continuous waves resulting in complex wave patterns and complicated fluctuations, especially for the quite low fd and large Ad. A possible route from solitary waves to chaos via bifurcations and mode competitions is therefore suggested on the basis of these observations.
Zhang
Likun
L
Institute of Acoustics, Nanjing University, Nanjing 210093, China. zhanglikun@nju.org.cn
Wang
Xinlong
X
Tao
Zhiyong
Z