  We investigate the propagation of an ultrashort optical pulse using
Fokas-Lenells equation (FLE) under varying dispersion, nonlinear effects and
perturbation. Such a system can be said to be under soliton management (SM)
scheme. At first, under a gauge transformation, followed by shifting of
variables, we transform FLE under SM into a simplified form, which is similar
to an equation given by Davydova and Lashkin for plasma waves, we refer to this
form as DLFLE. Then, we propose a bilinearization for DLFLE in a non-vanishing
background by introducing an auxiliary function which transforms DLFLE into
three bilinear equations. We solve these equations and obtain dark and
anti-dark one-soliton solution (1SS) of DLFLE. From here, by reverse
transformation of the solution, we obtain the 1SS of FLE and explore the
soliton behavior under different SM schemes. Thereafter, we obtain dark and
anti-dark two-soliton solution (2SS) of DLFLE and determine the shift in phase
of the individual solitons on interaction through asymptotic analysis. We then,
obtain the 2SS of FLE and represent the soliton graph for different SM scheme.
Thereafter, we present the procedure to determine N-soliton solution (NSS) of
DLFLE and FLE. Later, we introduce a Lax pair for DLFLE and through a gauge
transformation we convert the spectral problem of our system into that of an
equivalent spin system which is termed as Landau-Lifshitz (LL) system. LL
equation (LLE) holds the potential to provide information about various
nonlinear structures and properties of the system.
