We apply the two-variable )--expansion method to construct new exact traveling wave solutions with parameters of the nonlinear potential Boussinesq and ZKBBM equations. This method can be thought of as the generalization of the well-known )---expansion method given recently by Wang and co-workers (2008). When the parameters are replaced by special values, the well-known solitary wave solutions of this equation are rediscovered from the traveling waves. It is shown that the proposed method provides a more general powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

Keywords: The two-variable )—expansion method, the nonlinear potential Boussinesq and ZKBBM equations.