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The European Physical Journal D

, Volume 59, Issue 1, pp 23–36 | Cite as

Coarsening and frozen faceted structures in the supercritical complex Swift-Hohenberg equation

  • L. GelensEmail author
  • E. Knobloch
Regular Article

Abstract.

The supercritical complex Swift-Hohenberg equation models pattern formation in lasers, optical parametric oscillators and photorefractive oscillators. Simulations of this equation in one spatial dimension reveal that much of the observed dynamics can be understood in terms of the properties of exact solutions of phase-winding type. With real coefficients these states take the form of time-independent spatial oscillations with a constant phase difference between the real and imaginary parts of the order parameter and may be unstable to a longwave instability. Depending on parameters the evolution of this instability may or may not conserve phase. In the former case the system undergoes slow coarsening described by a Cahn-Hilliard equation; in the latter it undergoes repeated phase-slips leading either to a stable phase-winding state or to a faceted state consisting of an array of frozen defects connecting phase-winding states with equal and opposite phase. The transitions between these regimes are studied and their location in parameter space is determined.

Keywords

Modulational Instability Optical Parametric Oscillator Phase Gradient Rotating Wave Phase Jump 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Applied Physics and PhotonicsVrije Universiteit BrusselBrusselBelgium
  2. 2.Department of PhysicsUniversity of CaliforniaBerkeleyUSA

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