Dichromatic soliton molecule modeled by two cubic–quintic Ginzburg–Landau equations coupled with a cross phase modulation term

The occurrence of pulsating behavior is a prevalent phenomenon that has been observed in various nonlinear dissipative systems, hence showcasing an extensive variety of intriguing nonlinear dynamics. Herein, we undertake a numerical analysis to investigate the evolution dynamics of dichromatic soliton molecule (DSM) which consist of two dissipative solitons with varying frequencies. The simulation model is built upon two cubic-quintic Ginzburg-Landau equations that are coupled with a cross phase modulation (XPM) term. The results reveal a transition from a stationary DSM to various forms of pulsating DSMs. In addition, the influence of the coupling parameters has also been discussed. These findings show the existence of out-of-phase temporal vibrations trajectories due to the presence of unbalanced nonlinear gain, resembling the behavior observed in coupled harmonic mechanical oscillators. Our investigation is expected to enhance the comprehension of the fundamental physical mechanisms involved, hence promoting subsequent experimental inquiries into the complex dynamics of soliton molecules in dissipative systems.