Exact solutions of the one-dimensional modified complex Ginzburg–Landau equation

The one-dimensional modified complex Ginzburg–Landau (MCGL) equation is studied using a method derived from the Painlevé test for integrability and Hirotaʹs bilinear formalism. Exact solutions are expressed in terms of pulses, periodic unbounded waves, fronts, sources and sinks. The degeneracies of the MCGL equation have been examined as well as several of their solutions.