Abstract
In this paper, two generalized fifth-order nonlinear evolution equations are introduced and investigated: One is (1+1)-dimensional, the other is (2+1)-dimensional. The Hereman-Nuseir method is used to derive the multiple kink solutions and singular kink solutions, and the conditions for the cases of complete integrability of these two equations. Meanwhile, it is found that these equations have completely different dispersion relations and physical structures. The corresponding graphs with specific parameters are given to show the effectiveness and validness of the obtained results.