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In this article, a new dynamical system equation is constructed, named the (3+1)-dimensional Hirota-bilinear-like equation. The new ‘like’ equation has more nonlinear terms than the original equation while they have the same bilinear form. The generalized Hirota bilinear operator and its logarithmic transformation are applied to obtain the new ‘like’ equation and to find its solutions. Some different types of symbolic solutions are obtained, which are the lump solutions and the lump-kink-type rogue wave solutions. The propagation images of the lump waves and the interaction which is between the lump-type waves and two-kink soliton-waves are simulated to analysis the shapes and movements of these solutions.

In this article, a new dynamical system equation is constructed, named the (3+1)-dimensional Hirota-bilinear-like equation. The new 'like' equation has more nonlinear terms than the original equation while they have the same bilinear form. The generalized Hirota bilinear operator and its logarithmic transformation are applied to obtain the new 'like' equation and to find its solutions. Some different types of symbolic solutions are obtained, which are the lump solutions and the lump-kink-type rogue wave solutions. The propagation images of the lump waves and the interaction which is between the lump-type waves and two-kink soliton-waves are simulated to analysis the shapes and movements of these solutions. • A new (3+1)-dimensional Hirota-bilinear-like equation is constructed. • The bilinear form was constructed based on the generalized Hirota bilinear operator. • The lump solutions and the lump-kink-type solutions are obtained and plotted. [ABSTRACT FROM AUTHOR]