We study mechanisms of multi-wavelength emissions (X-ray, GeV and TeV gamma-rays) from the gamma-ray binary LS~5039. This paper is composed of two parts. In the first part, we report on results of observational analysis using four year data of fermi Large Area Telescope. Due to the improvement of instrumental response function and increase of the statistics, the observational uncertainties of the spectrum in $sim$100-300 MeV bands and $>10$GeV bands are significantly improved. The present data analysis suggests that the 0.1-100GeV emissions from LS~5039 contain three different components; (i) the first component contributes to $<$1GeV emissions around superior conjunction, (ii) the second component dominates in 1-10GeV energy bands and (iii) the third component is compatible to lower energy tail of the TeV emissions. In the second part, we develop an emission model to explain the properties of the phase-resolved emissions in multi-wavelength observations. Assuming that LS~5039 includes a pulsar, we argue that both emissions from magnetospheric outer gap and inverse-Compton scattering process of cold-relativistic pulsar wind contribute to the observed GeV emissions. We assume that the pulsar is wrapped by two kinds of termination shock; Shock-I due to the interaction between the pulsar wind and the stellar wind and Shock-II due to the effect of the orbital motion. We propose that the X-rays are produced by the synchrotron radiation at Shock-I region and the TeV gamma-rays are produced by the inverse-Compton scattering process at Shock-II region.
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