On the stability of localized structures in the complex Ginzburg–Landau equation

We study analytically the asymptotic linear stability of fixed-modulus dissipative–dispersive localized solutions of the one-dimensional quintic complex Ginzburg–Landau (GL) equation in the region where there exists a coexistence of homogeneous attractors. The linear analysis gives an indication for the existence of pulses with an oscillating modulus