Annularly and radially phase-modulated spatiotemporal necklace-ring patterns in the Ginzburg–Landau and Swift–Hohenberg equations

Abstract

Annularly and radially phase-modulated spatiotemporal necklace-shaped patterns (SNPs) in the complex Ginzburg-Landau (CGL) and complex Swift-Hohenberg (CSH) equations are theoretically studied. It is shown that the annularly phase-modulated SNPs, with a small initial radius of the necklace and modulation parameters, can evolve into stable fundamental or vortex solitons. To the radially phase-modulated SNPs, the modulated "beads" on the necklace rapidly vanish under strong dissipation in transmission, which may have potential application for optical switching in signal processing. A prediction that the SNPs with large initial radii keep necklace-ring shapes upon propagation is demonstrated by use of balance equations for energy and momentum. Differences between both models for the evolution of solitons are revealed.