Pattern Selection and Spatiotemporal Transition to Chaos in the Ginzburg-Landau Equation

Abstract

It is shown that a modulationally unstable pattern is selected and propagates into an initially unstable motionless state in the one-dimensional generalized Ginzburg-Landau equation. A further spatiotemporal transition occurs with a sharp interface from the selected unstable pattern to a stabilized pattern or a chaotic state. The distinct transition makes a coherent structure coexist with a chaotic state.