Solitary pulses in linearly coupled cubic–quintic Ginzburg–Landau equations

A dynamical model based on a symmetric system of linearly coupled complex Ginzburg–Landau (CGL) equations is introduced, with cubic–quintic (CQ) nonlinearities in the dissipative and conservative parts of the equations. In nonlinear optics, the system models a twin-core fiber laser. We focus on the study of spontaneous symmetry breaking in solitary pulses (SPs). For this purpose, direct simulations are used, aiming to reach stable SP states as attractors of the system. Different initial conditions lead to a set of established states, including symmetric and asymmetric stationary SPs, split pulses (ones with separated centers of the two components), and breathers (oscillating SPs which feature long-period beatings). Two diagrams of the stable states are constructed, starting from initial conditions of two different types. The system demonstrates hysteresis, which chiefly includes bistability, and in some cases tristability.