Nilpotent singular points and compactons

In this paper, dynamical system theory is applied to several types of fully nonlinear wave equations. These equations can be reduced to planar polynomial differential systems by transformation of variables. We treat these polynomial differential systems by phase space analytical technique. The results of our study demonstrate that there exist close connection between nilpotent singular points and compactons. Moreover, we find some new elliptic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points. Two new compactons induced by singular elliptic are also obtained.