Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 6 August 2019
Issue publication date: 11 September 2019
Abstract
Purpose
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.
Design/methodology/approach
Based on Hirota’s bilinear theory, a direct method is used to examine the lump solutions of these two equations.
Findings
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.
Originality/value
The dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional KP-type nonlinear wave equations.
Keywords
Acknowledgements
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.
Citation
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
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited