Propagation dynamics of multipole solitons generated in complex fractional Ginzburg–Landau systems

Based on the complex Ginzburg–Landau equation, propagation dynamics of multipole solitons generated in the dissipative system are numerically investigated by the split-step Fourier method. The effect of the value of the different Lévy indexes on stability regions of the soliton has been explored. In addition, we observe domains of different outcomes of the evolution of the input beam in the parameter plane of linear loss coefficient or diffraction gain coefficient and cubic gain coefficient. The results show that the evolution can lead to three different outcomes: decay, development into stable single soliton, expansion into the spreading pattern. We also study the evolution of multipole solitons generated with larger quintic loss coefficients and find that the input splits into the symmetrical fragments in the initial propagation. It is also demonstrated that two solitons or three solitons merge into the single soliton. Meanwhile, the relationship of merging distance with Lévy index and initial amplitude is also given.