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The world of the complex Ginzburg-Landau equation

Igor S. Aranson and Lorenz Kramer

Igor S. Aranson

  • Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439

Lorenz Kramer

  • Physikalisches Institut, University of Bayreuth, D-95440 Bayreuth, Germany

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Rev. Mod. Phys. 74, 99 – Published 4 February, 2002

DOI: https://doi.org/10.1103/RevModPhys.74.99

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. The authors give an overview of various phenomena described by the complex Ginzburg-Landau equation in one, two, and three dimensions from the point of view of condensed-matter physicists. Their aim is to study the relevant solutions in order to gain insight into nonequilibrium phenomena in spatially extended systems.

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Rev. Mod. Phys. 74, 99– Published 4 February, 2002

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