Multibump, blow-up, self-similar solutions of the complex Ginzburg-Landau equation

In this article we construct, both asymptotically and numerically, multibump, blow- up, self- similar solutions to the complex Ginzburg - Landau equation ( CGL) in the limit of small dissipation. Through a careful asymptotic analysis, involving a balance of both algebraic and exponential terms, we determine the parameter range over which these solutions may exist. Most intriguingly, we determine a branch of solutions that are not perturbations of solutions to the nonlinear Schrodinger equation ( NLS); moreover, they are not monotone, but they are stable. Furthermore, these axisymmetric ring- like solutions exist over a broader parameter regime than the monotone profile.