Phase turbulence in the Complex Ginzburg--Landau equation via Kuramoto--Sivashinsky phase dynamics

Guillaume van Baalen

We study the Complex Ginzburg--Landau initial value problem ${\partial }_{t}u=(1+i\alpha ){\partial }_x^{2}u+u-(1+i\beta )u|u{|}^2$, $u(x,0)=u_0(x)$ for a complex field $u\in \mathbf{C}$, with $α,β\…