This work presents novel perception into the optical solitons of the cubic-quartic nonlinear Schrödinger’s equation (CQ-NLSE) by introducing the cubic-quintic-septic-nonic (CQSN) form of self-phase modulation (SPM). The proposed model has a significant role in physics and engineering and it is considered the equation of pulses dissemination in optical communication. To extract the optical solitons such as the bright, kink, periodic and singular solitons, the Kudrashov’s method and extended hyperbolic function method (EHFM) are applied for the first time. The results show that these methods are suitable, productive and competent to find the solutions for such kind of nonlinear evolution equations (NLEEs) in optical fibers and nonlinear sciences. Moreover, for physical illustration of obtained solutions, some 3d, contour and 2d graphs are plotted which shed light on the differences between the solutions obtained …
