Dissipative solitons of the discrete complex cubic-quintic Ginzburg-Landau equation

We study, analytically, the discrete complex cubic-quintic Ginzburg-Landau (dCCQGL) equation with a non-local quintic term. We find a set of exact solutions which includes, as particular cases, bright and dark soliton solutions, constant magnitude solutions with phase shifts, periodic solutions in terms of elliptic Jacobi functions in general forms, and various particular periodic solutions.