In the present paper, an integrable semi-discrete analogue of the one-dimensional coupled Yajima--Oikawa system, which is comprised of multicomponent short-wave and one component long-wave, is proposed by using Hirota's bilinear method. Based on the reductions of the B\"{ a}cklund transformations of the semi-discrete BKP hierarchy, both the bright and dark soliton (for the short-wave components) solutions in terms of pfaffians are constructed.
Categories: nlin.SI math-ph math.MP