The evolution of the two-point functions of autonomous one-dimensional single-species reaction-diffusion systems with nearest-neighbor interaction and translationally-invariant initial conditions is investigated. It is shown that the dynamical phase structure of such systems consists of five...

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is shown that turning on the reactions which generate...

A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of the average number of the particles tend to infinity, so...

It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbour interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different models is investigated. Double-shocks may vanish, and the...

A family of multispecies drop-push systems on a one-dimensional lattice is investigated. It is shown that this family is solvable in the sense of the Bethe ansatz, provided a nonspectral matrix equation is satisfied. The large-time behavior of the conditional probabilities, and the dynamics of...

A two-parameter family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice is introduced, which contains the asymmetric simple exclusion process and the drop-push model as particular cases. The process is rewritten in terms of boundary conditions, and the...