“…[8][9][10][11][12][13][14] Therefore, nonlinear optics has gradually become an important sub-discipline in optical research, and study of higher-order nonlinear effects on pulse transmission, mode-locked lasers and other applications is of great scientific significance. [15][16][17][18][19][20][21][22][23] On the other hand, optical solitons, known as localized electromagnetic waves, have the ability to propagate steadily through nonlinear materials with dispersion effects. Research of optical solitons is a significant subject in nonlinear optics, which is great potential in quantum information processing, optical communication, and optical switching, etc.…”