%0 Journal Article
%T Solitons in the one-dimensional forest fire model
%A Per Bak
%A Kan Chen
%A Maya Paczuski
%J Physics
%D 2000
%I arXiv
%R 10.1103/PhysRevLett.86.2475
%X Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as solitons, resembling shocks in Burgers turbulence. The branching of solitons, creating new fires, is balanced by the pair-wise annihilation of oppositely moving solitons. Two distinct, diverging length scales appear in the limit where the growth rate of trees, $p$, vanishes. The width of the solitons, $w$, diverges as a power law, $1/p$, while the average distance between solitons diverges much faster as $ d \sim \exp({\pi}^2/12p)$.
%U http://arxiv.org/abs/cond-mat/0009205v2