Lump and lump-multi-kink solutions in the (3+1)-dimensions

Based on the test function method, we present the necessary and sufficient conditions for deriving lump solutions to four special types of (3+1)-dimensional nonlinear evolution equations. Compared with previous research, the number of the algebraic equations to be solved can be reduced. Moreover, we propose two approaches to construct lump-multi-kink solutions by virtue of two kinds of test functions. We prove that if the lump solutions to some special types of (3+1)-dimensional nonlinear evolution equations are derived, the lump-multi-kink solutions can be constructed, and the number of kink waves can be arbitrary. The lump solutions and lump-multi-kink solutions to the (3+1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation are given as illustrative examples. These approaches may provide support for the study of the existence of lump solutions and mixed solutions.