Periodic spatio-temporal oscillations governed by a globally controlled Ginzburg–Landau equation

A new type of periodic oscillations in a globally controlled subcritical cubic complex Ginzburg–Landau equation, formerly observed in numerical simulations, is explained and investigated analytically by means of a multiscale perturbation theory. Using an appropriate class of solutions of the nonlinear Schrödinger equation as a starting point, we construct a new class of asymptotic solutions of the cubic complex Ginzburg–Landau equation in the limit of large dispersion and nonlinear frequency shift.