Interaction solution to the (3+1)-D negative-order KdV first structure

We derive N-solitons and interaction solution for the (3+1)-D negative-order KdV first structure that arises in shallow-water waves. We use the bilinear scheme and the simplified Hirota technique for this solution. From the multiple solitons solution, we obtain a lump-shaped breather wave, a lump-shaped breather with a kink wave, and two lump-shaped breather waves from 2-solitons, 3-solitons, and 4-solitons, sequentially, by choosing complex conjugates of related parametric constants. Additionally, we show some novel interactions of the Jacobian elliptic transformation with periodic function, single soliton, and two solitons. Owing to these collisions, periodic waves with a kink wave, periodic breathers with a kink wave, and numerous bright and dark breather waves are created. We illustrate the properties of these solutions with 3D, density, and contour plots by selecting the appropriate values for the parameters. The obtained solutions will serve as milestones for studying the properties of nonlinear structures in the physical sciences and engineering fields.