We consider Complex Ginzburg-Landau equations with a polynomial nonlinearity in the real line. We use splitting-methods to prove well-posedness for a subset of almost periodic spaces. Specifically, we prove that if the initial condition has multiples of an irrational phase, then the solution of the equation maintains those same phases.

• 35K55 - Nonlinear parabolic equations
• 35K58 - Semilinear parabolic equations
• 47J35 - Nonlinear evolution equations