Fig. 1. Effect of parameter b1 on breather characteristics. (a) Akhmediev breather with b1=0.8;(b) Kuznetsov-Ma soliton with b1=1.25. The other parameters are a=0, c=1, a1=0, α4=1/32

Fig. 2. Breather and soliton conversion. (a) Breather for VH/κi≠VT/κr;(b) Soliton for VH/κi=VT/κr; (c) corresponding pulse distribution of the two cases at t=0

Fig. 3. Influence of parameter c on breather characteristic. (a) c=0.5; (b) c=0.8; (c) c=0.9; (d) corresponding pulse distribution of the three cases at t=0

Fig. 4. Influence of parameter a on soliton characteristics. (a) Oscillatory W-type soliton with a=-0.5; (b) W-type soliton with a=0.5; (c) corresponding pulse distribution of the two cases at t=0

Fig. 5. Effect of parameter α4 on breather characteristic. (a) General breathers with α4=1/16; (b) oscillatory W-type soliton with α4=1/64; (c) corresponding pulse distribution of the two cases at t=0

Fig. 6. Collision between two breathers

Fig. 7. Collisions between solitons and breathers. (a) W-type soliton and breather; (b) periodic soliton and breather

Fig. 8. Relationship curves between a1 and b1 for λ2=0.08+0.9i (the blue line) and λ2=0.08+1.0i (the red line)

Fig. 9. Two breathers parallel superimposition. (a) λ1=0.8756+1.8i; (c) λ1=2.2581+1.8i; (b) and (d) are the corresponding partial enlarged views of (a) and (c)

Fig. 10. Transmission characteristics of two-breather. (a) λ1=0.0276+0.9737i,λ2=0.08+0.9i; (b) λ1=0.0276+0.9737i,λ2=0.08+1.0i

Fig. 11. Degenerate solution of two-breather. (a) a=0,c=1,a1=0.03,b1=0.97,a2=0.03,b2=0.9701,α4=1/64; (b) a=0,c=1, a1=-1,b1=0.707,a2=-1,b2=0.7071,α4=1/16; (c) a=2,c=0.8,a1=-1,b1=0.707, a2=-1,b2=0.7071,α4=1/16