Dynamical behavior of traveling wave solutions for the K(2, 2) equation

In this paper, we discuss the qualitative behavior of degenerate singular points for the K(2, 2) equation. By analyzing the different dynamical behaviors of the singular system and its associated regular system, we come to the conclusion that for the singular system the smoothness property of its orbits, which have intersection point(s) with the singular straight line, will not be destroyed. Meanwhile, the corresponding smooth traveling wave solutions for the K(2, 2) equation are obtained.