Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation

Soliton solutions of the one-dimensional (1D) complex Ginzburg-Landau equations (CGLE) are analyzed. We have developed a simple approach that applies equally to both the cubic and the quintic CGLE. This approach allows us to find an extensive list of soliton solutions of the CGLE, and to express all these solutions explicitly. In this way, we were able to classify them clearly. We have found and analyzed the class of solutions with fixed amplitude, revealed its singularities, and obtained a class of solitons with arbitrary amplitude, as well as some other special solutions. The stability of the solutions obtained is investigated numerically.