By means of a special variable separation approach, a common formula with two arbitrary functions has been obtained for suitable physical quantity of (1+1)-dimensional model such as Boiti-Leon-Pempinelli-Spire system. Based on the derived formula, some significant types of solitons such as compacton, peakon, and loop solutions localized in space and periodical in time are simultaneously constructed from the (1+1)-dimensional soliton system by entrancing appropriate piecewise smooth functions and multivalued functions.