Traveling waves and defects in the complex Swift-Hohenberg equation

Abstract

The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and, as such, admits solutions in the form of traveling waves. The properties of these waves are systematically analyzed and the dynamics associated with sources and sinks of such waves investigated numerically. A number of distinct dynamical regimes is identified and analyzed using appropriate phase equations describing the evolution of long-wavelength instabilities of both the homogeneous oscillating state and constant amplitude traveling waves.