Phase dynamics in the complex Ginzburg–Landau equation

For <f>αβ>−1</f>, stable time periodic solutions <f>A(X,T)=AqeiqX+iωqT</f> are the locally preferred planform for the complex Ginzburg–Landau equation∂TA=A+(1+iα)∂X2A−(1+iβ)A|A|2.In order to describe the spatial global behavior, an evolution equation for the local wave number <f>q</f> can be derived formally. The local wave number <f>q</f> satisfies approximately a conservation law <f>∂τq=∂ξh(q)</f>. It is the purpose of this paper to explain the extent to which the conservation law is valid by proving estimates for this formal approximation. [Copyright &y& Elsevier]