We report quasi-periodic pulsations (QPPs) with double periods during three solar flares (viz. SOL2011-Feb-15T01:44, SOL2011-Sep-25T04:31, SOL2012-May-17T01:25). The flare QPPs were observed from light curves in Ly$alpha$, hard X-ray (HXR) and microwave emissions, with the Ly$alpha$ emission recorded by the Geostationary Operational Environmental Satellite, the HXR emission recorded by the Reuven Ramaty High-Energy Solar Spectroscopic Imager and the Fermi Gamma-ray Burst Monitor, and the microwave emission recorded by the Nobeyama Radio Polarimeters and Radioheliograph. By using the Markov chain Monte Carlo (MCMC) method, QPPs with double periods of about two minutes and one minute were first found in the Ly$alpha$ emission. Then using the same method, a QPP with nearly the same period of about two minutes was also found in HXR and microwave emissions. Considering the possible common origin (nonthermal electrons) between Ly$alpha$ and HXR/microwave emission, we suggest that the two-minute QPP results from the periodic acceleration of nonthermal electrons during magnetic reconnections. The ratio between the double periods in the Ly$alpha$ emission was found to be close to two, which is consistent with the theoretical expectation between the fundamental and harmonic modes. However, we cannot rule out other possible driving mechanisms for the one-minute QPPs in HXR/microwave emissions due to their relatively large deviations.
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