  The Aim of our study is to understand the variety of observed Lyman-alpha
(Lya) line profiles and strengths in Lyman Break Galaxies (LBGs) and Lya
emitters (LAEs), the physical parameters governing them, and hence deriving
constraints on the gas and dust content and stellar populations of these
objects.
  Using our 3D Lya radiation transfer code including gas and dust (Verhamme et
al. 2006), we fit 11 LBGs from the FORS Deep Field with redshifts between 2.8
and 5 observed by Tapken et al. (2007). A simple geometry of a spherically
expanding shell of HI is adopted.
  RESULTS : The variety of observed Lya profiles is successfully reproduced.
Most objects show outflow velocities of 150-200 km/s; two objects are most
likely quasi-static. The radial HI column density ranges from NH=2.10^{19} to
7.10^{20} cm^{-2}. Our Lya profile fits yield values of E(B-V)~0.05-0.2 for the
gas extinction. We find indications for a dust-to-gas ratio higher than the
Galactic value, and for a substantial scatter. The escape fraction of Lya
photons is found to be determined primarily by the extinction, and a simple fit
formula is proposed. Intrinsic EW(Lya)~50-100 Angstroms are found for 8/11
objects, as expected for stellar populations forming constantly over long
periods (> 10-100 Myr). In three cases we found indications for younger
populations. Correlations between the observed EW(Lya) and other observables
such as FWHM(Lya), E(B-V),SFR(UV) etc, are reproduced. We also show that there
is a clear overlap between LBGs and LAEs. Radiation transfer and dust effects
explain the increase of the LAE/LBG ratio, and a higher percentage of LBGs with
strong Lya emission with increasing redshift. [shortened]
