Instability of the steady states of some Ginzburg–Landau-like equations with real coefficients

Abstract

The instability of the steady states with nonconstant amplitude is analysed for a nonlocal Ginzburg–Landau equation with real coefficients and quasiperiodic boundary conditions. The results are obtained in terms of easily recognized, qualitative properties of the steady states. Some of the results are new, even for the standard (local) Ginzburg–Landau equation with real coefficients. A related Ginzburg–Landau equation coupled to a mean field is also considered that appears in the analyses of counter-propagating waves in extended systems, nonoscillatory instabilities with a conservation law, and viscous Faraday waves in large aspect ratio containers