Abstract
By using the bifurcation theory of dynamical systems to the generalized Kadomtsov–Petviashvili–Benjamin–Bona–Mahony equation, the existence of solitary wave solutions, compactons solution, non-smooth periodic cusp wave solutions and uncountably infinite many 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.
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