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

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」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.