Exact soliton solutions of the cubic-quintic complex Ginzburg-Landau equation

Abstract

Soliton solutions of the 1-D complex Ginzburg-Landau equations (CGLE) are analyzed. We apply the same approah to look for stationary solutions of both the cubic and quintic CGLE, and fing general solutions in both cases. We reveal the singularities of the general solutions and find some families of special solutions which exist at those values of the coefficients where the general solutions cannot be applied. The stability of the special solutions is investigated numerically.