Boundary Effects in The Complex Ginzburg-Landau Equation
Victor M. Eguiluz, Emilio Hernandez-Garcia, Oreste Piro (IMEDEA, Palma, de Mallorca, Spain)
TL;DR
This paper investigates how finite boundaries influence the behavior of the 2D complex Ginzburg-Landau equation, revealing new states and phenomena such as target-like solutions, boundary-induced synchronization, and defect anchoring.
Contribution
It introduces the impact of finite geometries on the complex Ginzburg-Landau equation, demonstrating boundary-induced states and dynamics not observed in infinite domains.
Findings
Target-like solutions emerge under Dirichlet boundary conditions.
Synchronization of plane waves occurs due to boundary effects.
Defects are anchored by shock lines near boundaries.
Abstract
The effect of a finite geometry on the two-dimensional complex Ginzburg-Landau equation is addressed. Boundary effects induce the formation of novel states. For example target like-solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Nonlinear Photonic Systems · Quantum optics and atomic interactions