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In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund transformation, Lax pair and infinite conservation laws. It is proved that the equation is completely integrable in Lax pair sense. Based on the Hirota bilinear method and the test function method, high-order lump solutions, high-order lump-kink type [Formula: see text]-soliton solutions, high-order lump-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] type soliton solutions, [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] type soliton solutions and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] type soliton solutions [Formula: see text] for this equation are obtained with the help of symbolic computation. Via three-dimensional plots and contour plots with the help of Mathematics, analyses for the obtained solutions are presented, and their dynamic properties are discussed. Many dynamic models can be simulated by nonlinear evolution equations, and these graphical analyses are helpful to understand these models.

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