Can someone show that it's possible to find a solution of the kind:
$\Phi(x,t)=R(x,t)\exp[i\Psi(x,t)]$
of the complex Ginzburg - Landau equation:
$\frac{\partial{\Phi}}{\partial{t}}=(1+ia)\frac{\partial^2{\Phi}}{\partial{x}^2}+\Phi-(ib-1)|\Phi|^2\Phi$
assuming that $R(x,t)$ and $\Psi(x,t)$
are defined as real - valued functions?
Thanks