TY - JOUR

T1 - Localized structures in a nonlinear wave equation stabilized by negative global feedback

T2 - One-dimensional and quasi-two-dimensional kinks

AU - Rotstein, Horacio G.

AU - Zhabotinsky, Anatol A.

AU - Epstein, Irving R.

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevE.74.016612

DO - 10.1103/PhysRevE.74.016612

M3 - Article

AN - SCOPUS:33746618914

VL - 74

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

M1 - 016612

ER -