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Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

Jin-Jin Mao (School of Mathematics, China University of Mining and Technology, Xuzhou, China)
Shou-Fu Tian (School of Mathematics, China University of Mining and Technology, Xuzhou, China)
Xing-Jie Yan (School of Mathematics, China University of Mining and Technology, Xuzhou, China)
Tian-Tian Zhang (School of Mathematics, China University of Mining and Technology, Xuzhou, China)

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