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

Journal Article · Sat Jul 15 00:00:00 EDT 2006 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PHYSREVE.74.016612· OSTI ID:20860623

Rotstein, Horacio G; Zhabotinsky, Anatol A; Epstein, Irving R ^[1]

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1. Department of Mathematics and Center for Biodynamics, Boston University, Boston, Massachusetts 02215 (United States)

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.

• OSTI ID: 20860623
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 74, Issue 1; Other Information: DOI: 10.1103/PhysRevE.74.016612; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BORN-INFELD THEORY
FEEDBACK
KLEIN-GORDON EQUATION
MATHEMATICAL EVOLUTION
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PERTURBATION THEORY
PHASE TRANSFORMATIONS
SINE-GORDON EQUATION
STABILIZATION
TWO-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS