Abstract
In this article, we study Lie point symmetries, closed-form invariant solutions, and dynamics of exact solitons to an extended (3+1)-dimensional Jimbo-Miwa (JM) equation by employing the Lie symmetry method. Under the resulting symmetries, the extended JM equation is reduced to lower-dimensional equations. We exploit the travelling wave ansatz to determine closed-form invariant solutions of the reduced equations. The physical interpretations of the obtained solutions are exhibited in the forms of single solitons, multi-wave solitons, multiple solitons with parabolic waves, oscillating lump solitons, triply solitons, and double solitons via numerical simulation for adequate choices of the involved arbitrary constants through the mathematical software Wolfram Mathematica. These constructed solutions can help us better understand interesting nonlinear complex phenomena and mechanisms.