New lump and interaction soliton, N-soliton solutions and the LSP for the (3 + 1)-D potential-YTSF-like equation

•We establish some exact solutions for the (3+1)-D YTSF-like equation with p=3 and p=5 which are considered based on the generalized Hirota bilinear method.•Through a specific computations with Maple software, M-soliton solutions, lump solution and three classes of interaction solutions of the YTSF-like equation expressed explicitly.•We employ the linear superposition principle to determine N-soliton wave solutions of the YTSF-like equation.•The evaluated solutions are explained through various sketches in two, three-dimensional, density, and curve plots. In this work, we established some exact solutions for the (3 + 1)-dimensional potential-Yu-Toda-Sasa-Fukuyama (YTSF)-like equation with p=3 and p=5 which are considered based on the generalized Hirota bilinear method. Depending on the analysis of Hirota operator, a generalized bilinear differential equation of the YTSF-like equation type is formulated. Furthermore, through a specific computations with Maple software, M-soliton solutions, lump solution and three classes of interaction solutions of the YTSF-like equation expressed explicitly. Moreover, we employ the linear superposition principle (LSP) to determine N-soliton wave solutions of the (3 + 1)-dimensional YTSF-like equation. The studied equation describes the physical characterization of model for investigating the dynamics of solitons and nonlinear waves in fluid dynamics, plasma physics and weakly dispersive media. Moreover, a few key differences are presented, which exits in the literature and the current offer. The evaluated solutions are explained through various sketches in two, three-dimensional, density, and curve plots of their real, imaginary, and absolute value. The computational applied schemes’ performance is tested to illustrate their powerful, and effectiveness for handling many nonlinear evolutions equations.