Localized structures in a nonlinear wave equation stabilized by negative global feedback: One-dimensional and quasi-two-dimensional kinks

Horacio G. Rotstein, Anatol A. Zhabotinsky, Irving R. Epstein

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study the evolution of fronts in a nonlinear wave equation with global feedback. This equation generalizes the Klein-Gordon and sine-Gordon equations. Extending previous work, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the classical case (with no global feedback), leading in most cases to a localized solution; i.e., the stabilization of one phase inside the other. The nature of the localized solution depends on the strength of the global feedback as well as on other parameters of the model.

Original languageEnglish (US)
Article number016612
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number1
DOIs
StatePublished - 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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