The purpose of this paper is to find homoclinic breather waves, rogue waves and soliton waves for a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation, which can be used to describe the propagation of weakly nonlinear dispersive long waves on the surface of a fluid.
The authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional gKP equation.
The results imply that the gKP equation admits rogue waves, homoclinic breather waves and soliton waves. Moreover, the authors also find that rogue waves can come from the extreme behavior of the breather solitary wave. The authors analyze the propagation and interaction properties of these solutions to better understand the dynamic behavior of these solutions.
These results may help us to further study the local structure and the interaction of waves in KP-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.
This work was supported by the Jiangsu Province Natural Science Foundation of China under Grant No. BK20181351, the Research and Practice of Educational Reform for Graduate students in China University of Mining and Technology under Grant No. YJSJG_2018_036, 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.
Feng, L.-L. and Zhang, T.-T. (2019), "Homoclinic breather waves, rogue waves and solitary waves for a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 2, pp. 553-568. https://doi.org/10.1108/HFF-07-2018-0381Download as .RIS
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