The traveling wave solutions for generalized Benjamin-Bona-Mahony equation

The traveling wave solutions of generalized BBM equation with any power are investigated. The existence and numbers of bell solitary wave solutions, kink solitary wave solutions and periodic wave solutions are obtained by using qualitative theory of planar dynamical system. The new exact expressions of peaked light solitary wave solutions, valley dark solitary wave solutions and kink solitary wave solutions are given by the method of undetermined coefficient. Further, by numerical simulating, the behavior of these exact traveling solutions are analyzed. In visually, we verify that the result about existence of traveling wave solutions for generalized BBM equation is right. Moreover, the convexity, monotonicity and number of critical points for period solutions of generalized BBM equation have been discussed. The integral expressions and corresponding orbit curves of period solutions are studied.