Fig. 1. Illustration of partially PT-symmetric potential. (a) Real part of potential; (b) imaginary part of potential

Fig. 2. Symmetry breaking bifurcation diagrams of partially PT-symmetric solitons with different values of Lévy indexes. (a)(b) Real and imaginary parts of propagation constant for α=2.0; (c)(d) real and imaginary parts of propagation constant for α=1.5; (e)(f) real and imaginary parts of propagation constant for α=1.0

Fig. 3. Partially PT-symmetric solitons and symmetry breaking solutions corresponding to different values of soliton powers with α=1.5. (a1)-(a3) Real part, imaginary part, and amplitude profiles of partially PT-symmetric solitons at P=0.5; (b1)-(b3) real part, imaginary part, and amplitude profiles of partially PT-symmetric solitons at P=1.5; (c1)-(c3) real part, imaginary part, and amplitude profiles of symmetry breaking solution at P=1.5

Fig. 4. Power curves at different Lévy indexes. (a) Real part of power curve changes with Lévy index; (b) imaginary part of power curve changes with Lévy index; (c) critical power changes with Lévy index, where the circles represent critical power corresponding to Lévy index shown by vertical dotted line

Fig. 5. Unstable growth rates and unstable boundary. (a) Maximum unstable growth rate of partially PT-symmetric soliton changes with Lévy index and soliton power; (b) unstable boundary of partially PT-symmetric solitons in the parameter plane of α-P, the circles represent critical power of symmetry breaking of the partially PT-symmetric solitons

Fig. 6. Evolution of stable partially PT-symmetric soliton with α=1.5, β=1.24, and P=0.5. (a) Spectrum of linear stability analysis; (b)-(d) intensity of soliton at different transmission distances; (e) dependence of intensity of the soliton on transmission distances; (f) stable evolution is displayed by iso-intensity surface (value of iso-intensity is 0.06)

Fig. 7. Evolution of the unstable partially PT-symmetric soliton with α=1.5, β=1.3, and P=1.5. (a) Spectrum of linear stability analysis; (b)-(d) intensity of soliton at different transmission distances; (e) dependence of intensity of the soliton on transmission distances; (f) unstable evolution is displayed by iso-intensity surface (the value of iso-intensity is 0.03)

Fig. 8. Evolution of symmetry breaking solution with α=1.5, β=1.33-i0.009, and P=1.5. (a) Spectrum of linear stability analysis of symmetry breaking solution; (b)-(d) intensity of symmetry breaking solution at different transmission distances; (e) dependence of intensity of symmetry breaking solution on transmission distances; (f) unstable evolution is displayed by iso-intensity surface (the value of iso-intensity is 0.07)