  Amplitude death, which occurs in a system when one or more macroscopic
wavefunctions collapse to zero, has been observed in mutually coupled
solid-state lasers, analog circuits, and thermoacoustic oscillators, to name a
few applications. While studies have considered amplitude death on oscillator
systems and in externally forced complex Ginzburg-Landau systems, a route to
amplitude death has not been studied in autonomous continuum systems. We derive
simple analytic conditions for the onset of amplitude death of one macroscopic
wavefunction in a system of two coupled complex Ginzburg-Landau equations with
general nonlinear self- and cross-interaction terms. Our results give a more
general theoretical underpinning for recent amplitude death results reported in
the literature, and suggest an approach for tuning parameters in such systems
so that they either permit or prohibit amplitude death of a wavefunction
(depending on the application). Numerical simulation of the coupled complex
Ginzburg-Landau equations, for examples including cubic, cubic-quintic, and
saturable nonlinearities, is used to illustrate the analytical results.
