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Characteristics of the breather waves, rogue waves and solitary waves in an extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation

Hui Wang (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)
Yi Chen (School of Mathematics, China University of Mining and Technology, Xuzhou, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 5 August 2019

Abstract

Purpose

The purpose of this paper is to study the breather waves, rogue waves and solitary waves of an extended (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation, which can be used to depict many nonlinear phenomena in fluid dynamics and plasma physics.

Design/methodology/approach

The authors apply the Bell’s polynomial approach, the homoclinic test technique and Hirota’s bilinear method to find the breather waves, rogue waves and solitary waves of the extended (3 + 1)-dimensional KP equation.

Findings

The results imply that the extended (3 + 1)-dimensional KP equation has breather wave, rogue wave and solitary wave solutions. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior.

Originality/value

These results may help us to further study the local structure and the interaction of solutions in KP-type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of such equations.

Keywords

Acknowledgements

The authors express their sincere thanks to the editor and reviewers for their valuable comments. This work was supported by the Fundamental Research Funds for the Central Universities under the Grant No. 2019QNA35, the Jiangsu Province Natural Science Foundation of China under Grant No. BK20181351, Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant No. SJKY19_1876, the “Qinglan Engineering project” of Jiangsu Universities, the National Natural Science Foundation of China under Grant No. 11301527 and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.

Citation

Wang, H., Tian, S.-F. and Chen, Y. (2019), "Characteristics of the breather waves, rogue waves and solitary waves in an extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 8, pp. 2964-2976. https://doi.org/10.1108/HFF-01-2019-0047

Publisher

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Emerald Publishing Limited

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