Five reliable integration architectures are adopted in this paper,
namely the unified Riccati equation expansion, the modified simple
equation, the extended simplest equation, the generalized sub-ODE, and
the new extended auxiliary equation approaches for the extraction of
optical soliton solutions and other solutions in birefringent fibers
without four-wave mixing (FWM) terms for the Biswas-Arshed model. Bright
soliton, kink and dark soliton, singular soliton, hyperbolic wave, a
periodic wave, elliptic function solutions of Wierestrass and Jacobian,
and other solutions have been derived as a result. The conditions of
their existence are also revealed. Also, the results obtained are
compared with the well-known ones listed for the Biswas-Arshed model in
birefringent fibers without FWM. The amplitude and intensity diagrams of
some of the attained solutions in this study are portrayed by providing
the appropriate values of the parameters included in the solutions for
physical description.