Velocity and diffusion coefficient of $A+A\leftrightarrow A$ reaction fronts in one dimension

We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get correct value of the front diffusion coefficient.