Traveling wave solutions in the Burridge-Knopoff model

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The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the form of self-sustained shock waves traveling with constant speed which depends only on the amount of accumulated stress in front of the wave. For a wide class of initial conditions the behavior of the system is determined by these shock waves and the dynamics of the system can be expressed in terms of their motion. The solutions in the form of the periodic wave trains and sources of counterpropagating waves are analyzed. It is argued that depending on the initial conditions the system will either tend to synchronize or exhibit chaotic spatiotemporal behavior.

Original languageEnglish (US)
Pages (from-to)3847-3857
Number of pages11
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
StatePublished - 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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