Pattern selection at an instability with broadened sidebands

The spatiotemporal pattern formation in the vicinity of a codimension-2 bifurcation with a quartic eigenvalue spectrum is studied. The interaction of modes on long time scales is derived. It is shown that a nonlinear focusing process selects a narrow band of modes and suppresses the other unstable modes. On an intermediate length scale, a travelling wave pattern emerges. Its modulations on long space scales are governed by a dispersive complex Ginzburg-Landau equation. (C) 2001 Elsevier Science B.V. All rights reserved