The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of the (2 + 1)- and the (3 + 1)-dimensional breaking soliton equations. By this application, we obtain one-wave, two-wave and three-wave solutions for these equations.
