Exact solutions in front propagation problems with superdiffusion

Vladimir Volpert*, Y. Nec, A. A. Nepomnyashchy

*Corresponding author for this work

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

Front propagation in a number of reaction-superdiffusion problems is studied. Specifically, traveling wave propagation, domain wall pinning, and systems of waves governed by a bistable single equation as well as FitzHugh-Nagumo equations are considered. The reaction terms in the equations are taken in the form of piecewise linear functions, which allow for exact solutions to be obtained. The effect of superdiffusion on front propagation is discussed.

Original languageEnglish (US)
Pages (from-to)134-144
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Volume239
Issue number3-4
DOIs
StatePublished - Jan 1 2010

Keywords

  • Exact solution
  • FitzHugh-Nagumo equations
  • Front
  • Reaction-diffusion problem
  • Superdiffusion

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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