Lump-type solution and breather lump–kink interaction phenomena to a ($$\mathbf{{3{\varvec{+}}1}}$$)-dimensional GBK equation based on trilinear form

Abstract

In this paper, the multivariate trilinear operators in the ($$3+1$$)-dimensional space are applied to a ($$3+1$$)-dimensional GBK equation. The resulting trilinear form is used to study its wave dynamics. Particularly, we generate a type of new interaction solutions between breather lump-type solitons and other multi-kink solitons, thereby formulating a kind of breather lump–kink solitons. By setting time constants, we change the coordinates of kink solitons to make them collide with the breather lump-type soliton, during which breather lump-type soliton is swallowed eventually by those kink solitons. The evolution behaviours of the breather lump–kink solitons are depicted by plotting 3-D and density graphs from the perspective of wave characteristics.