Abstract: For the generalized Serre-Green-Naghdi equations with surface tension, by using the methodologies of dynamical systems and singular traveling wave theory developed Li \& Chen [2007] to their travelling wave systems, in different parameter conditions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) are obtained. More than 26 explicit exact parametric representations are given. It is interesting to find that this fully nonlinear water waves equation has coexistence of uncountably infinitely many smooth solitary wave solutions or uncountably infinitely many pseudo-peakon solutions with periodic solutions or compacton solutions. Differing from the well-known peakon solution of the Camassa-Holm equation, the generalized Serre-Green-Naghdi equations have four new forms of peakon solutions.
