  The thermal production mechanism of dark matter is attractive and
well-motivated by predictivity. A representative of this type of dark matter
candidate is the canonical, weakly interacting massive particles. An
alternative is semi-annihilating dark matter, which exhibits different
phenomenological aspects from the former example. In this study, we constructed
a model of dark matter semi-annihilating into a pair of anti-dark matter and a
Majoron based on a global $U(1)_{B-L}$ symmetry, and show that
semi-annihilation induces the core formation of dark matter halos, which can
alleviate the so-called small-scale problems. In addition, the box-shaped
spectrum of neutrinos was produced by the subsequent decay of the Majoron. This
can be a distinctive signature of the dark matter in the model. We find a
parameter space where the produced neutrinos can be detected by the future
large-volume neutrino detector Hyper-Kamiokande. We also compared the dark
matter scenario with the case of halo core formation by the strongly
self-interacting dark matter.
