Solitons in the one-dimensional forest fire model

Per Bak; Kan Chen; Maya Paczuski

doi:10.1103/physrevlett.86.2475

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Solitons in the one-dimensional forest fire model

Per Bak·Kan Chen·Maya Paczuski

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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(π^2/12p)$.

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Per Bak, Kan Chen, Maya Paczuski. 2000-11-15. Solitons in the one-dimensional forest fire model. https://doi.org/10.1103/physrevlett.86.2475

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