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]

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