Periodic and Chaotic Exploding Dissipative Solitons

Abstract

This article shows for the first time the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order non-linear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modeling soliton transmission lines. This counter-intuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations leading to chaos (chaotic explosions). This periodic behavior is persistent even when small amounts of noise are added to the system. Since for ultrashort optical pulses it is necessary to include these higher-order effects, it is conjectured that the predictions can be tested in mode-locked lasers.