In this paper, we have acquired the periodic type and cross-kink wave solutions. In this paper, we use the Hirota bilinear method. With the help of the symbolic calculation and applying the used method, we solve the (2+1)-dimensional Breaking Soliton (BS) equation. We obtain some periodic wave and cross-kink wave that have greatly enriched the existing literature on the BS equation. All solutions have been verified back into its corresponding equation with the aid of the Maple package program via the three-dimensional images and density images with the help of Maple, the physical characteristics of these waves are described very well. These will be widely used to describe many interesting physical phenomena in the fields of gas, plasma, optics, acoustics, heat transfer, fluid dynamics, classical mechanics and so on.