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. (c) 2021 Elsevier B.V. All rights reserved.