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In this paper, the solitary waves in superfluid Bose-Fermi mixture are investigated under the limited case of a BEC regime, a BCS regime and unitarity. By using the transverse perturbation method, a coupled Korteweg de Vries (KdV) equation for the nonlinear solitary waves is derived. It is found that the scattering length between bosons and fermions has strong effect on the characters of the coupled solitary wave.

We study the tunneling dynamics of superfluid Fermi gases in an optical lattice from BEC to unitarity regime. Four different cases are found, namely Josephson oscillations (JO), oscillating-phase-type self-trapping (OST), running-phase-type self-trapping (RST) and self-trapping (ST). We find that the s-wave scattering length has a crucial role on the tunneling dynamics. Periodic modulation can also affect the tunneling phenomena, for example, in the high frequency modulation, the optical lattice is splitted at the zero points of the zeroth order Bessel function J0 and strong suppression of tunneling by the modulation is observed at these points.

We investigate the process of production of ultracold molecules in an ultracold bosonic system with particle interaction via designing a magnetic field pulse train near a Feshbach resonance. This technique offers a high conversion efficiency up to 100% by tuning the pulse durations appropriately. The molecular conversion efficiency is related to the duration of each pulse, which can be derived analytically. It is found that the conversion efficiency is insensitive to the first pulse, highly sensitive to the second one, and very insensitive to the third one. The effects of particle interaction on conversion process are discussed as well.