Solitons in the one-dimensional forest fire model

Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as s olitons, resembling shocks in Burgers turbulence. The branching of solitons , creating new fires, is balanced by the pairwise annihilation of oppositel y moving solitons. Two distinct, diverging length scales appear in the limi t where the growth rate of trees, p, vanishes. The width of the solitons, w ,diverges as a power law, lip, while the average distance between solitons diverges much faster as d similar to exp(pi (2)/12p).