Dynamic evolution of pulsating solitons in a dissipative system with the gain saturation effect

We numerically investigate the dynamic evolution of pulsating solitons based on complex cubic-quintic Ginzburg-Landau equation with gain dynamics effects. We show that an additional soliton can be generated by the disturbance caused by a dispersion wave emitted by a single-period pulsating soliton and these solitons form soliton molecule. More complicated oscillating processes, such as snaking pulsation and double-periodic pulsation are actuated by periodic collision of the entangled solitons. Moreover, the dispersive wave, caused by high gain parameters and the soliton collision, appears periodically which is in sync with the pulsating process. These results are consistent with the recent experiments of soliton pulsations measured by dispersive Fourier transform techniques, and will stimulate further experimental research of the complex multi-soliton bunches in dissipative systems.