A nonlinear Schrödinger equation describing the polarization mode in an optical fiber which involves different physical terms such as quintic nonlinearity, self-steepening effect, and self-frequency shift is investigated in the present paper. The study goes on by adopting a field function and effective ansatzes to arrive at a highly nonlinear ODE which is formally solved with the help of the modified Kudryashov and expa-function methods. As a result, a series of chirped optical solitons along with nonlinear chirps is retrieved, confirming the fantastic performance of schemes.
