The World of the Complex Ginzburg-Landau Equation

Abstract

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity and Bose-Einstein condensation to liquid crystals and strings in field theory. Our goal is to give an overview of various phenomena described the complex Ginzburg-Landau equation in one, two and three dimensions from the point of view of condensed matter physicists. Our approach is to study the relevant solutions to get an insight into nonequilibrium phenomena in spatially extended systems.

Submitted to Reviews of Modern Physics, reduced resolution figures

References in corpus (4)

• Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation
• Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation
• Defect Statistics in the Two Dimensional Complex Ginsburg-Landau Model
• Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation

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• Suppression of macroscopic oscillations in mixed populations of active and inactive oscillators coupled through lattice Laplacian
• A three-level linearized difference scheme for the coupled nonlinear fractional Ginzburg-Landau equation
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• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap
• State Diagram of the Non-Reciprocal Cahn-Hilliard Model and the Effects of Symmetry
• The Berry connection of the Ginzburg-Landau vortices
• Multiscale modelling of tumour growth induced by circadian rhythm disruption in epithelial tissue
• Vortex unbinding transition in nonequilibrium photon condensates
• Modeling polymerization of microtubules: a quantum mechanical approach
• Stationary modulated-amplitude waves in the 1-D complex Ginzburg-Landau equation
• Regulating protocols of globally coupled continuum systems: Effects on dynamics and thermodynamics
• Optical resonators constitute a universal spin simulator
• Quantized Vortex Dynamics of the Nonlinear Wave Equation on the Torus
• Breaking chirality in nonequilibrium systems on the lattice
• Diffusive stability of convective Turing patterns
• Nutational Two-Dimensional Structures in Magnets
• Dynamics of vortices for the Complex Ginzburg-Landau equation
• The biological frontier of pattern formation
• Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions
• The energy flow of dissipative systems on infinite lattices
• Global well-posedness for cubic NLS with nonlinear damping
• On the backward behavior of some dissipative evolution equations
• Non-Lagrangian approach for coupled complex Ginzburg-Landau systems with higher order-dispersion
• Phase-Diffusion Equations for the Anisotropic Complex Ginzburg-Landau Equation