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 Bifurcations and Exact Travelling Wave Solutions of M-N-Wang Equation mao wei hong Keywords:Solitary wave solution, periodic peakon, anti-peakon, Mikhailov-Novikov-Wang integrable equation Abstract: By using the method of dynamical systems to Mikhailov-Novikov-Wang Equation, through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system of the derivative $\phi(\xi)$ of the wave function $\psi(\xi)$. Under different parameter conditions, for $\phi(\xi)$, exact explicit solitary wave solutions, periodic peakon and anti-peakon solutions are obtained. By integrating known $\phi(\xi)$, nine exact explicit traveling wave solutions of $\psi(\xi)$ are given.