Abstract
Using generalized bilinear equations, we construct a (3+1)-dimensional Jimbo–Miwa-like equation which possesses the same bilinear type as the standard (3+1)-dimensional Jimbo–Miwa equation. Classes of lump-type solutions and interaction solutions between lump-type and kink solutions to the resulting Jimbo–Miwa-like equation are generated through Maple symbolic computation. We discuss the conditions guaranteeing analyticity and positiveness of the solutions. By taking special choices of the involved parameters, 3D plots are presented to illustrate the dynamical features of the solutions.