Construction of Lump and optical solitons solutions for (3 + 1) model for the propagation of nonlinear dispersive waves in inhomogeneous media

Our work aims to investigate new solutions for the (3 + 1)-dimensional Extended Date–Jimbo–Kashiwara–Miwa Equation which characterize the physical phenomena owing to the inhomogeneities of media. By using the Hirota—method with the aid of a quadratic test function, we derived a new Lump—soliton solution that localized in all directions in space and time. A class of 1-soliton solution and more-soliton solution are explored using the improved tanh–coth method and the improved tan–cot method. The sequel in these solutions demonstrate a valuation of physical phenomenon. Two, three-dimensional, contour and density plots are presented to illustrate the behaviors of the solitons.