A solvable aggregation-annihilation chain model with n species

The aggregation-annihilation processes involving n species are discussed by means of meanfield theory. We propose a sort of solvable chain-reaction models in which n kinds of species are numbered, the irreversible aggregations occur only between similar species and the annihilations occur only between dissimilar species having adjacent numbers. Under constant aggregation and annihilation reaction rates and certain symmetric condition, the exact solutions of the models are obtained, which show that the kinetic exponents describing evolution behaviors of reactants at long time depend on reaction rates and the numbers of species in the reaction processes.