  In models of multi-component dark matter, the lighter component of dark
matter can be boosted by annihilations of the heavier state if mass splitting
is large enough. Such relativistic dark matter can be detectable via large
neutrino detectors such as Super-Kamiokande and IceCube. Moreover, if the
process is inelastic scattering and decay length of the produced particle is
short enough, another signature coming from the decay can also be detectable.
In this paper, we construct a simple two-component dark matter model with a
hidden U(1)_D gauge symmetry where the lighter component of dark matter has a
potential to improve the so-called small scale structure problems with large
self-interacting cross section. We estimate number of multi-Cherenkov ring
events due to both of the boosted dark matter and subsequent decay of the
particle produced by inelastic scattering at Hyper-Kamiokande future
experiment. Some relevant constraints, such as dark matter direct detection and
cosmological observations, are also taken into account. The numerical analysis
shows that some parameter space which can induce large self-interacting cross
section can give a few multi-Cherenkov ring events per year at
Hyper-Kamiokande.
