Abstract
The extension of exponential rational function method is obtained to construct a series of exact solutions for higher-dimensional Broer-Kaup-Kupershmidt (BKK) dynamical system. New and general solutions are found. The solutions reported in this work are kink solutions, anti-kink solutions and bright solutions. They are expressed in terms of rational exponential functions. A confrontation of our results with the well-known results are done and it comes from this study that the solutions obtained here are new. The mathematical method applied to search for our solutions can be used for other nonlinear partial differential equations. The graphics of the obtained solutions in this paper are shown.