Annihilation-diffusion processes: an exactly solvable model

A family of diffusion-annihilation processes is introduced, which is exactly solvable. This family contains parameters that control the diffusion- and annihilation- rates. The solution is based on the Bethe ansatz and using special boundary conditions to represent the reaction. The processes are investigated, both on the lattice and on the continuum. Special cases of this family of processes are the simple exclusion process and the drop-push model.