**Featured Application: The optical soliton solutions obtained in this research paper may be of concern and useful in many fields of science, such as mathematical physics, applied physics, nonlinear science, and engineering.**

**Abstract:** In this paper, the cubic-quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions. Two powerful methods, the - *m* + *<sup>G</sup>*- *G* improved expansion method and the exp(−*ϕ* (*ξ*)) expansion method are utilized to construct some novel solutions of the governing equations. The obtained optical soliton solutions are presented graphically to clarify their physical parameters. Moreover, to verify the existence solutions, the constraint conditions are utilized.

**Keywords:** cubic-quartic Schrödinger equation; cubic-quartic resonant Schrödinger equation; parabolic law
