  Theoretical methods for dealing with diffusion-controlled reactions
inevitably rely on some kind of approximation and to find the one that works on
a particular problem is not always easy. In here the approximation used by
Bogolyubov to study weakly non-ideal Bose gas, to be refereed to as weakly
non-ideal Bose gas approximation (WBGA), is applied in the analysis of of the
three reaction-diffusion models (i) A+A->0, (ii) A+B->0 and (iii)
A+A,B+B,A+B->0 (the ABBA model). The two types of WBGA are considered, the
simpler WBGA-I and more complicated WBGA-II. All models are defined on the
lattice to facilitate comparison with computer experiment (simulation). It is
found that the WBGA describes A+B reaction well, it reproduces correct d/4
density decay exponent. However, it fails in the case of the A+A reaction and
the ABBA model. (To cure deficiency of WBGA in dealing with A+A model the
hybrid of WBGA and Kirkwood superposition approximation is suggested.) It is
shown that the WBGA-I is identical to the dressed tree calculation suggested by
Lee in J. Phys. A 27, 2633 (1994), and that the dressed tree calculation does
not lead to the d/2 density decay exponent when applied to the A+A reaction, as
normally believed, but it predicts d/4 decay exponent. Last, the usage of the
small n_0 approximation suggested by Mattis and Glasser in Rev. Mod. Phys. 70,
979 (1998) is questioned if used beyond A+B reaction-diffusion model.
