Abstract
By using the bifurcation theory of dynamical systems, we study the generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili equation, the existence of solitary wave solutions, compacton solutions, periodic cusp 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 exact explicit parametric representations of the above waves are determined.
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