https://doi.org/10.1007/s100510050964
Convective and absolute instabilities in the subcritical Ginzburg-Landau equation
Instituto Mediterráneo de Estudios Avanzados, IMEDEA (:
) (CSIC-UIB), Campus Universitat
Illes Balears,
07071 Palma de Mallorca, Spain
Corresponding author: a pere@imedea.uib.es
Received:
17
December
1998
Published online: 15 October 1999
We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity.
PACS: 47.20.Ky – Nonlinearity (including bifurcation theory) / 47.54.+r – Pattern selection; pattern formation / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999
