  An efficient Monte Carlo simulation method for bosonic reaction-diffusion
systems which are mainly used in the renormalization group (RG) study is
proposed. Using this method, one dimensional bosonic single species
annihilation model is studied and, in turn, the results are compared with RG
calculations. The numerical data are consistent with RG predictions. As a
second application, a bosonic variant of the pair contact process with
diffusion (PCPD) is simulated and shown to share the critical behavior with the
PCPD. The invariance under the Galilean transformation of this boson model is
also checked and discussion about the invariance in conjunction with other
models are in order.
