Dynamical Analysis Of A Class Of Rotation-theta-equation

In this dissertation,we analyze the rotation-θ equation,which is the theta equation augmented with the Coriolis effect,induced by the earth rotation.The Rotation-θ equation is a generalization of a family of models(including the Rotation-CamassaHolm equation and the Rotation-Degasperis-Procesi).Our study is conducted via the bifurcation method and qualitative theory of dynamical systems.The existence of not only smooth solitary wave solution,periodic wave solution,but also peakon and periodic peakon solutions are given.