Static, oscillating modulus, and moving pulses in the one-dimensional quintic complex Ginzburg-Landau equation: An analytical approach

By means of a matching approach we study analytically the appearance of static and oscillating-modulus pulses in the one-dimensional quintic complex Ginzburg-Landau equation without nonlinear gradient terms. When considering nonlinear gradient terms the method enables us to calculate the velocities of the stable and unstable moving pulses. We focus on this equation since it represents a prototype envelope equation associated with the onset of an oscillatory instability near a weakly inverted bifurcation. The results obtained using the analytic approximation scheme are in good agreement with direct numerical simulations. The method is also useful in studying other localized structures like holes.