Optical variabilities in Be/X-ray binary system:GRO J2058+42

We present an analysis of long-term optical monitoring observations and optical spectroscopic observations of the counterpart to CXOU J205847.5+414637 (high mass X-ray binary system). We search for a variability in the light curve of Be star. We used differential magnitudes in the time series analysis. The variability search in the optical light curve was made by using different algorithms. The reduction and analysis of spectra were done by using MIDAS and its suitable packages. We have performed a frequency search which gave us the value 2.404 1/day. This value is attributed to the non-radial pulsation of Be star. H alpha emission line profiles always show double-peaked emissions with a mean equivalent width of 2.31 \pm 0.19 \AA ~and a peak separation of 516 \pm 45 km/s. This suggests that Be star disk is still present. CXOU J205847.5+414637 is in X-ray quiescent state.