Fisher waves in the strong noise limit

Phys Rev Lett. 2009 Sep 4;103(10):108103. doi: 10.1103/PhysRevLett.103.108103. Epub 2009 Sep 2.


We investigate the effects of a strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute the wave velocity in one and two spatial dimensions, for which we find a linear and a square-root dependence of the speed on the particle density. Instead of smooth sigmoidal wave profiles, we observe fronts composed of a few rugged kinks that diffuse, annihilate, and rarely branch; this dynamics leads to power-law tails in the distribution of the front sizes.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Diffusion
  • Linear Models
  • Models, Theoretical*
  • Quantum Theory
  • Stochastic Processes