The purpose of this study is to examine the lump solutions of the (3 + 1)-dimensional nonlinear evolution equations by considering a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and a (3 + 1)-dimensional variable-coefficient generalized B-type Kadomtsev–Petviashvili (vcgBKP) equation as examples.
Based on Hirota’s bilinear theory, a direct method is used to examine the lump solutions of these two equations.
The complete non-elastic interaction solutions between a lump and a stripe are also discussed for the equations, which show that the lump solitons are swallowed by the stripe solitons.
The dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional KP-type nonlinear wave equations.
This work was supported by the Jiangsu Province Natural Science Foundation of China under Grant No. BK20181351, the “Qinglan Engineering project” of Jiangsu Universities, the National Natural Science Foundation of China under Grant No. 11301527, the Fundamental Research Fund for the Central Universities under the Grant No. 2019QNA35, and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.
Mao, J.-J., Tian, S.-F., Yan, X.-J. and Zhang, T.-T. (2019), "Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 9, pp. 3417-3436. https://doi.org/10.1108/HFF-02-2019-0160
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