We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The coagulation (A+A to A) or the annihilation (A+A to 0) models can be mapped onto systems in which both processes are allowed. With the help of the coagulation-decoagulation model results for some death-decoagulation and annihilation-creation systems are given. We also find a reaction-diffusion system which is equivalent to the two-species annihilation model (A+B to 0). Besides we present numerical results of Monte Carlo simulations. An accurate description of the effects of the reaction rates on the concentration in one-species diffusion-annihilation model is made. The asymptotic behaviour of the concentration in the two-species annihilation system (A+B to 0) with symmetric initial conditions is studied.
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H. Simon (1995) studied this question.