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Faraday waves in Bose--Einstein condensate: From instability to nonlinear dynamics

We numerically study the dynamics of Faraday waves in a pancake-shaped Bose--Einstein condensate (BEC) subject to periodic modulation of the interaction. After the modulation starts, Faraday waves appear and, thereafter, the BEC enters the "nonlinear regime", in which several collective modes are excited. By maintaining the modulation without dissipation, the kinetic energy that contributes to the density gradient causes quasiperiodic motion and increases monotonically. In the nonlinear regime, the dips in the density similar to dark solitons move around in the BEC, intersecting with each other and maintaining their shapes. On the other hand, even by turning off the modulation, Faraday waves and the nonlinear regime appear. The kinetic energy converges to the statistical steady state. The calculation of the modulation with the dissipation illustrates the collapse and revival of Faraday waves. When the dissipation is small, the appearance and collapse of the Faraday waves and the nonlinear regime occur again.