Abstract
By using the bifurcation theory of dynamical systems to the Zakharov-Kuznetsov-Modified Equal-Width (ZK-MEW) equation, we analysis all bifurcations and phase portraits in the parametric space, the existence of solitary wave solutions and uncountably infinite many smooth periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some explicit exact solution formulas are acquired for some special cases.
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