The superradiant instability of tiny-mass scalar fields around a rotating black hole provokes rich phenomena such as periodic occurrence of bose nova and complicated interactions of different unstable modes, if non-linear self-interactions of the scalar fields are taken into account. The very fascinating point of these phenomena is that they can be detected by gravitational waves and thereby, provide us a probe to string theory that is expected to produce a rich spectrum of tiny mass axions by compactification. In the present talk, after overviewing the basics of superradiant instability and its relevance to string theory, I explain the results of our recent work on this problem by numerical simulations in collaboration with Hirotaka Yoshino. In particular, we point out the sensitivity of the phenomena to the axion mass and decay constant, and discuss the observability of gravitational waves from these phenomena by LIGO and the future GW interferometers.