Fig. 1. Linear band structure and Anderson mode. (a) The first 80 Anderson modes form band structures; (b)‒(f) No.1, 2, 3, 4, 70 Anderson modes, their eigenvalues b are -7.7075, -7.6364, -7.6363, -7.6243, and 2.4271, respectively

Fig. 2. Power curves and partial solitons of soliton families originating from Anderson modes. (a) P-b curve of the disordered soliton family originating from the first Anderson mode, with the shaded area representing the first energy band; (b) corresponding to the soliton profile marked with a equilateral triangle (propagation constant b=-9) in Fig. 2(a). (c) P-b curve of the disordered soliton family originating from the fourth Anderson, illustrated by the power curve near the band; (d)(e)(f) soliton contours marked with circular (b=-7.63), square (b=-7.68), and inverted triangle (b=-7.90) in Fig. 2(c), remaining parameters c₁=1 and c₂=-0.1

Fig. 3. Power curves and partial solitons of the first type of high-order solitons. (a) P-b curves of the first class of multi-peaked solitons; (b) solitons of the branch Ⅰ and branch Ⅱ when b=-9.1; (c) solitons of the branch Ⅲ and branch Ⅳ when b=-9.1; (d) solitons of the branch Ⅴ and branch Ⅵ when b=-9.1; (e) solitons of the branch Ⅶ and branch Ⅷ when b=-9.1 remaining parameters c₁=1 and c₂=-0.1

Fig. 4. Relationship between perturbation growth rate and propagation constant of the first type of high-order soliton family, as well as the transmission diagram of some solitons. (a) Relationship between the perturbation growth rate and the propagation constant of the first kind of higher-order solitons; (b) transmission simulation of solitons in branch Ⅰ when b=-7.763; (c)(d) solitons of the branch Ⅰ and branch Ⅴ when b=-9.1, remaining parameters c₁=1 and c₂=-0.1

Fig. 5. Power curves and partial solitons of the second type of high-order soliton. (a) P-b curves of the second class of multi-peaked solitons; (b) solitons of the branch Ⅰ and branch Ⅱ when b=-8.2; (c) solitons of the branch Ⅲ and branch Ⅳ when b=-8.2; (d) solitons of the branch Ⅴ and branch Ⅵ when b=-8.2; (e) solitons of the branch Ⅶ and branch Ⅷ when b=-8.2, remaining parameters c₁=1 and c₂=-0.1

Fig. 6. Relationship between perturbation growth rate and propagation constant of the second type of high-order soliton family, as well as the transmission diagram of some solitons. (a) Relationship between the perturbation growth rate and the propagation constant of the second kind of higher-order solitons; (b) soliton of the branch Ⅰ when b=-8.2; (c)(d) solitons of the branch Ⅴ and branch Ⅶ when b=-8.2, remaining parameters c₁=1 and c₂=-0.1

Fig. 7. Power curves of self focusing solitons and partial solitons. (a) P-b curve of the self-focusing solitons; (b) solitons of the Ⅰ , Ⅱ , Ⅲ and Ⅳ branches when b=-4, remaining parameters c₁=-1 and c₂=0.1