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Abstract The central target of this work is to extract some novel exact solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) for the incompressible fluid. By applying the weight algorithm (WA) and linear superposition principle (LSP), we construct two sets of the complexiton solutions, which are the non-singular complexiton and singular complexiton solution via introducing the pairs of the conjugate parameters. In addition, we also explore the complex N -soliton solutions (CNSSs) via the Hirota bilinear equation (HBE) that is developed by the Cole-Hopf transform (CHT). The outlines of the corresponding exact solutions are presented graphically. As far as the information currently available, the derived solutions in this exploration are all new and are expected to enable us to investigate the dynamic characteristics of the considered equation better.
Wang et al. (Wed,) studied this question.