Solitons in the one-dimensional forest fire model

Details Solitons in the one-dimensional forest fire model Solitons in the one-dimensional forest fire model

2000-09-14

arxiv.org/abs/cond-mat/0009205v2

Physics

Condensed Matter

Statistical Mechanics

4 pages with 2 figures included

Scientific paper

10.1103/PhysRevLett.86.2475

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)$.

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