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.
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Acknowledgements
The work was supported in part by NSFC (61572095, 61877007, 11371326, 11301331, 11371086, 11571079 and 51771083), NSF under the Grant (DMS-1664561), Natural Science Fund for Colleges and Universities of Jiangsu Province under the Grant (17KJB110020), Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT under Grant (No. 2017XKZD11).
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Gai, L., Ma, WX. & Li, M. Lump-type solution and breather lump–kink interaction phenomena to a (\(\mathbf{{3{\varvec{+}}1}}\))-dimensional GBK equation based on trilinear form. Nonlinear Dyn 100, 2715–2727 (2020). https://doi.org/10.1007/s11071-020-05554-1
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DOI: https://doi.org/10.1007/s11071-020-05554-1