Dynamics of breather waves, lump-kink solutions and interaction solutions for a (3+1)-dimensional generalized shallow water waves equation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 June 2023
Issue publication date: 21 July 2023
Abstract
Purpose
This paper aims to study the breather, lump-kink and interaction solutions of a (3 + 1)-dimensional generalized shallow water waves (GSWW) equation, which describes water waves propagating in the ocean or is used for simulating weather.
Design/methodology/approach
Hirota bilinear form and the direct method are used to construct breather and lump-kink solutions of the GSWW equation. The “rational-cosh-cos-type” test function is applied to obtain three kinds of interaction solutions.
Findings
The fusion and fission of the interaction solutions between a lump wave and a 1-kink soliton of the GSWW equation are studied. The dynamics of three kinds of interaction solutions between lump, kink and periodic waves are discussed graphically.
Originality/value
This paper studies the breather, lump-kink and interaction solutions of the GSWW equation by using various approaches and provides some phenomena that have not been studied.
Keywords
Acknowledgements
This work is supported by the Program for Young Innovative Research Team in Shandong University of Political Science and Law and the Project of Shandong University of Political Science and Law Scientific Research Program (No. 2022Z05A).
Citation
Liu, N. (2023), "Dynamics of breather waves, lump-kink solutions and interaction solutions for a (3+1)-dimensional generalized shallow water waves equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 9, pp. 3272-3285. https://doi.org/10.1108/HFF-04-2023-0221
Publisher
:Emerald Publishing Limited
Copyright © 2023, Emerald Publishing Limited