Abstract: The traveling wave solutions and the dynamical properties
of Equation $K(n,-n,2n)$ were studied in terms of the bifurcation
theory of dynamic systems and of the qualitative theory. Based on
the characters of an integrable system, the solitary traveling wave
solutions, uncountably infinite many smooth periodic wave solutions
and non-smooth periodic traveling wave solutions of the system were
obtained. According to the relationship between traveling waves and
phase orbits, that changes of parameters led to the transitions of
traveling wave solutions of different types were revealed.

Key words: solitary wave, periodic wave, cusp wave, smooth wave, traveling wave, solitary wave, periodic wave, cusp wave, smooth wave