Solitons in the one-dimensional forest fire model

Abstract

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 $d\sim \exp ({\pi }^2/12p)$.

4 pages with 2 figures included

References in corpus (1)

• Scale Dependent Dimension in the Forest Fire Model

Cited by in corpus (1)

• Synchronization and Coarsening (without SOC) in a Forest-Fire Model