This paper recovers a full spectrum of optical solitons that are generated by the combined effects of dispersion and nonlinearity of the pulse propagation. The quadratic–cubic form of the nonlinear refractive index is incorporated in the governing nonlinear Schr¤odinger equation, which governs the dynamics of the soliton transmission across trans-continental and transoceanic distances. The model is considered with a nonlinear chromatic dispersion that is required to sustain for smooth transmission of soliton pulses in optical fibers, couplers, PCF, magneto-optic waveguides, crystals, metamaterials, metasurfaces, birefringent fibers, DWDM systems and other form of waveguides. Solitons in birefringent fibers as well as solitons in polarization preserving fibers are considered. The governing model is treated with Hamiltonian type perturbation terms. The perturbation terms are with full intensity. The model is studied for the intensity count m = 1. The adopted integration algorithm is the sine-Gordon equation method that reveals single form soliton solutions as well as dual-form soliton solutions. These solitons are dark soliton, singular soliton, bright soliton and combo singular soliton. Also, dark soliton represents a kink/anti-kink solitary wave or a shock wave in fluid dynamics. The respective constraint conditions are also in place to guarantee the existence of such solitons.
- Quadratic–cubic nonlinearity