Abstract
The ( G ′ ∕ G ) -expansion approach is an efficient and well-developed approach to solve nonlinear partial differential equations. In this paper, the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is investigated by using this approach, which describes the (2+1)-dimensional interaction of the Riemann wave propagated along the y -axis with a long wave propagated along the x -axis and can be considered as a model for the incompressible fluid. With the aid of symbolic computation, a family of exact solutions are obtained in forms of the hyperbolic functions and the trigonometric functions. When the parameters are selected special values, non-traveling wave solutions are also presented, and these gained solutions have abundant structures. The figures corresponding to these solutions are illustrated to show the particular localized excitations and the interactions between two solitary waves.
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