Fig. 1. Transmission evolution diagrams of light beam in different media. (a) FEAB in free space; (b) soliton in saturated nonlinear medium

Fig. 2. Interaction between FEAB and soliton at different phase differences. (a) Q=0; (b) Q=π

Fig. 3. Propagation of breathing soliton with different phase differences. (a) Q=-π/2; (b) Q=π/2

Fig. 4. Variation curves of characteristic parameters of the breathing soliton. (a) Oscillation transmission diagram of the breathing soliton; (b) variation curve of the average peak intensity of the breathing soliton with R when Q=0; (c) variation curve of the average peak intensity of the breathing soliton with R when Q=π; (d) peak position of breathing soliton under different phase differences

Fig. 5. Interaction of strong energy FEAB and soliton. (a) Intensity ratio is 50%, Q=0; (b) intensity ratio is 100%, Q=0; (c) intensity ratio is 50%, Q=π; (d) intensity ratio is 100%, Q=π

Fig. 6. Interaction of FEAB and soliton with different β. (a) Q=0; (b) Q=π

Fig. 7. Interaction of weak energy double FEABs and soliton. (a) Q=0; (b) Q=π

Fig. 8. Interaction of double FEABs and soliton at different initial intervals. (a) Q=0; (b) Q=π

Fig. 9. Interaction of double FEABs and soliton under different initial amplitude ratios. (a) Q=0; (b) Q=π