The Traveling Wave Solutions Of K(n, -n, 2n) Equation And Its Dynamical Behaviors

By using the bifurcation theory of dynamical systems and qualitative theory, this paper presents the dynamical behavior and traveling wave solutions of K(n,-n, 2n) equation. Based on characters of an integral system, the paper obtains its solitary wave solutions and uncountable infinite smooth and non-smooth periodic wave solutions. The paper demonstrates the relationship between changes of parameters and transition of different types of traveling wave solutions. In addition, the bifurcation values of different traveling wave solution are given. The paper further explains why "compacton" and "peakon" appear. Finally, some explicit travelling wave solutions are also given. With the help of the dynamical theory, some mistakes from the exact explicit solutions are found. Therefore, it is very necessary to understand the dynamical behavior of the traveling wave solutions. At last, the correctness of conclusions are tested by the use of numerical simulation.