Fig. 1. One-breather solution of NLSE. (a) a1=-0.5, b1=0.8; (b) a1=0.5, b1=1

Fig. 2. Peregrine soliton solution. (a) x1=0, t1=0; (b) x1=3, t1=3

Fig. 3. Collision of double breather. (a) b1=0.8; (b) b1→1; (c) avoid the collision of double breather

Fig. 4. Collision and separation of breathers. (a) Double Akhmediev breather collision; (b) double Akhmediev breather separation; (c) collision between Akhmediev breather and Kuznetsov-Ma soliton

Fig. 5. Generation and separation of second-order rouge waves. (a) Second-order rouge waves; (b) two-dimensional diagram; (c) separation

Fig. 6. Double breather collision. (a) κ1∶κ2=2κ∶κ; (b) κ1∶κ2=3κ∶2κ; (c) κ1∶κ2=4κ∶3κ

Fig. 7. Two breathers parallel superimposed with l1=-1.1705+1.4i and l2=-0.5+0.4i. (a) x1=0, x2=0; (b) partial enlargement; (c) x1=-2, x2=2

Fig. 8. Collisions of third-order breathers. (a) Double collision; (b) triple collision; (c) degeneration

Fig. 9. Generation and separation of third-order rouge waves. (a) Third-order rouge waves; (b) contours; (c) separation

Fig. 10. Third-order breather collision. (a) κ1∶κ2∶κ3=2∶3∶5 and κ1=0.8; (b) κ1∶κ2∶κ3=2∶3∶5 and κ1=0.6; (c) κ1∶κ2∶κ3=3∶2∶1 and κ1=1.8

Fig. 11. Third-order breather parallel transmission. (a) x1=0, x2=0, x3=0; (b) partial enlargement; (c) x1=-4, x2=0, x3=4

Fig. 12. Fourth-order breather interaction. (a) Double collision; (b) fourfold collision

Fig. 13. Degenerate breather. (a) Superposition of Akhmediev breather and Kuznetsov-Ma soliton degenerate state; (b) degenerate Akhmediev breather

Fig. 14. Generation of fourth-order rouge wave. (a) Fourth-order rouge waves; (b) two-dimensional diagram; (c) contour map

Fig. 15. Separation of fourth-order rouge wave. (a) Once separation; (b) twice separation

Fig. 16. Contour map of fourth-order breather interaction. (a) κ1∶κ2∶κ3∶κ4=1∶3∶5∶7; (b) κ1∶κ2∶κ3∶κ4=2∶4∶6∶8

Fig. 17. Third-order breather parallel transmission. (a) x1=0, x2=0, x3=0, x4=0; (b) partial enlargement; (c) x1=-6, x2=-2, x3=2, x4=6