Onset of Chaos in the Generalized Ginzburg-Landau Equation

Abstract

Study of chaos in the generalized Ginzburg-Landau equation (GLE)

$$ {\text{iu}}_{\text{t}} + {\text{u}}_{{\text{xx}}} + 2\left| {\text{u}} \right|^{\text{2}} {\text{u}} = {\text{i}} \in _1 {\text{u}} - {\text{i}} \in _3 \left| {\text{u}} \right|^2 {\text{u}} + {\text{i}} \in _2 u_{{\text{xx}}} $$

((1))

is a subject of great current interest, see, e.g., Refs. 1–6. We will consider Eq. (1) with the periodic boundary condition

$$ {\text{u(x)}} = {\text{u(x}} + 2\pi /{\text{k}}). $$

((2))