Bifurcations of travelling wave solutions for the K(n,-n,2n)K(n,-n,2n) equations

By using the bifurcation theory of dynamical systems to the K(n,-n,2n)K(n,-n,2n) equations given by Wazwaz, the existence of solitary wave solutions, solitary cusp wave solutions, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.