The traveling wave solutions and the dynamical propertiesof Equation $K(n,-n,2n)$ were studied in terms of the bifurcationtheory of dynamic systems and of the qualitative theory. Based onthe characters of an integrable system, the solitary traveling wavesolutions, uncountably infinite many smooth periodic wave solutionsand non-smooth periodic traveling wave solutions of the system wereobtained. According to the relationship between traveling waves andphase orbits, that changes of parameters led to the transitions oftraveling wave solutions of different types were revealed.