Abstract
•Solitons in birefringent fibers are studied analytically.•Four forms of nonlinear refractive index are considered.•Cubic-quartic dark and singular optical solitons are presented.
This paper applies exp-function expansion algorithm to secure to cubic-quartic dark and singular optical solitons in birefringent fibers that are studied with four forms of nonlinear refractive index. These solitons are listed along with their existence criteria and are also classified.