From the point of view of the extended simple equation method, multiple new private distinct types for the cubic-quartic optical soliton birefringent fibers with four forms nonlinear refractive index have been extracted. The suggested model has vital effective effect in all modern telecommunications process. The suggested method which has invited for this purpose examined previously for many other nonlinear problems arising in various branches of science and continuously gives good results. We will implement this method to extracting multiple new private types for the cubic-quartic soliton with its four different forms of the NLSE which are, the cubic-quartic in polarization-preserving fibers with the kerr-low nonlinearity, quadratic-cubic law nonlinearity, parabolic law nonlinearity and non-local law nonlinearity. Actual comparison between our achieved results and that realized previously by other authors has been established.